
Glass ___ 



Book. 






Copyright K?_ 



COPYRIGHT DEPOSIT. 



KNITTING CALCULATIONS 



A Cross - indexed Text Book of Practical 
Problems in Flat and Rib Knitting on tbe 
Inter-relation of Yarn Number ; Diameter ; 
Needles per Inch ; Stitches; Needle Speed, 
Production in Pounds, Square Yards, Linear 
Yards and Dozens of Garments; Weight of 
Fabric, Tensile Strength Both Ways, Width, 
Thickness and Appearance ; with chapters on 
Yarn Counts and their Conversion ; Single 
Equivalent of Multiple Yarns ; Proportions of 
Yarns in Multiple Thread Work ; Winder 
Capacity; Fabric Analysis, Single and Multiple 
Thread, Common Stitch and Warp; Miscellan- 
eous Problems ; and so on. 



Written for 

TEXTILE WORLD 

By 

ERNEST TOMPKINS, M. E. 

[Sibley College, Cornell University] 

Author of " The Science of Knitting " and numerous 
Articles on the Technology of Knitting 

Formerly Managerand Treasurer of Tompkins Bros. Co., Troy, N.Y. 

Knitting Expert for Wildman Mfg. Co., Norristown, Pa. 

Knitting Expert for U. S. Tariff Board, 1911 



NEW YORK 

BRAGDON, LORD & NAGLE CO., Publishers 

334 FOURTH AVENUE 






Copyrighted, 1922 , 

Bragdon, Lord &. Nagle Co., New York 






The Abbott Press 
New York 



MAR 20 i922 
©CU654984 






PREFACE 

It was at one time — and for a considerable time — the 
author's duty to travel from knitting mill to knitting mill ; and 
he was struck by the general loss to the industry due to lack 
of knowledge of what constituted good general practice in the 
knitting room. In one mill the yarn was too heavy for the 
gage, in another it was too light; in one the needle speed was 
too high, and in another it was too low. The situation seemed 
to be well expressed by a passage in Polibio's charming 
account of the naval battles of the Romans and Carthagenians, 
a little book which was sometimes carried for pastime on those 
travels : "I have recorded these things in order that those who 
shall read our history may know that there are available to men 
two means of guidance. The one by their own misfortune — 
the other by the misfortune of others. Certainly the first is 
more powerful, but not without danger to him who experiences 
it; the second, although it may not be so potent, is much more 
excellent on the score of being free from any danger. For 
which reason no one who can help it follows the first method 
which involves suffering and danger. But every one voluntarily 
desires the latter, because by this, without danger he is able to 
shape his course." 

This book enables the knitter to shape his course by basing 
it on the experience of others. The rules given herein are 
derived from voluminous notes made during many years and 
from extensive experimental work with different gages, yarns 
and stitches in order to round out the information collected in 
the various mills of the country. 

A great proportion of the problems, instead of being worked 
out for this book, are problems which were previously solved 
to meet some actual requirement; so, if it is true that history 
repeats itself, they should be of practical use. The other 
problems have been originated to fill the evident gaps which 
practical needs had not yet reached. The whole collection is 
believed to cover with a considerable degree of thoroughness 
the needs of the knitter, who, the author hopes, will thereby 
shape his course without danger. 



FOREWORD 



How To Use This Book 

THIS is essentially a hand book of informa- 
tion and calculations which will be used 
principally in the routine of daily work. To 
make it easy to find any particular calculation, 
and with the least possible delay, the author has 
prepared a very complete index which will be 
found among the back pages. Each subject in 
the index bears a number which corresponds 
with the black-face number found in the text 
covering that subject. Many pages of the text 
contain more than one calculation and users of 
the book will find this system of subject num- 
bering saves much time as against the usual 
method of page indexing. 



Knitting Calculations 

(1) Many of us remember the introduction of weather 
calculations. Before that we guessed at the weather, were satisfied 
with our guessing, and scoffed at the very idea of calculating 
about it. How could one calculate about anything depending 
on so many indeterminate circumstances? Consequently, when 
weather forecasts were based on calculations, instead of guesses, 
we received them with due incredulity. We expected each one 
to go wrong, and those which did go wrong were promptly 
pointed to as evidence of the absurdity of attempting to calcu- 
late about something not susceptible of calculation. The fore- 
caster and his forecasts were an inexhaustible source of jokes. 
But the conditions are different now. Altho there are still some 
who joke about the weather forecasts, the public as a whole 
has learned to respect the calculated forecasts and to scorn the 
mere guesses. The daily paper which does not print the fore- 
casts where they may readily be found is not considered much 
of a paper; for everybody wants to know what the weather is 
going to be. The mariner, the farmer, the traveler, the business 
man, even the lady who has calls to make or the child who 
wants to give a party consults the calculated forecast. 

Many lessons may be drawn from this bit of history. We 
may learn that a subject involving numerous apparently inde- 
terminate factors may be susceptible of calculation, provided 
the calculations are based on the most determinate factors and 
proper allowance is made for the other factors. We may learn 
that an innovation which appears crude at first may develop a 
surprising degree of reliability. We may learn that the benefit 
to be gained by the substitution of calculation for guessing can 
not be judged adequately until we make use of the calculations. 

Let us endeavor to bear these lessons in mind in our con- 
sideration of knitting calculations. First, since the factors 
involved in knitting are more determinate than those involved 
in the weather, knitting calculations are bound to come into 
use. Therefore, the proper attitude is not to oppose them or 
to ridicule them more than they deserve, but to accept them 
for what they are worth. What are they really worth ? 

5 



6 KNITTING CALCULATIONS 

(2) The Worth of Knitting Calculations 

To attempt to say what knitting calculations are really 
worth is to attempt to prophesy; for that worth depends on 
general use of the calculations, and general use depends on the 
availability of much more data than we have at hand. For 
instance, the diameter of knitting yarn, one of the most neces- 
sary factors, is available to only a slight extent, and even then, 
not with a considerable degree of reliability. So, instead of 
endeavoring to tell the worth of knitting calculations, we may 
better discuss the dependability of such calculations as may be 
made with the data at hand. This is no excuse for dropping the 
subject altogether; for complete data will not be collected until 
there is a demand for it, and the demand will not be made until 
the insufficiency of the present data is realized thru actual use 
of it. If automobilists had not used the poor roads they would 
not have agitated for good ones. Here follows a comparison of 
the calculated and actual results in a test case. A little piece 
of yarn was given to a calculator, who measured it by coiling it, 
and made his calculations. Some cones of the yarn were given 
to a practical knitter to be made into fabric. After the calcula- 
tions were made, the yarn was reeled to determine its number 
and the fabric was measured and weighed. All the calculated 
results are given and they are compared with what actual meas- 
urements were made. 

(3) Comparison of Calculated and Actual Results 

Calculated Actual Difference % 

y 2 Coils 38.5 

Yarn 13.2 14. — .8 — 5.7 

Cut 9. 10. — 1. —10. 

Stitches 36. 

Wales 19.25 18. + 1.25 + 6.95 

Courses 24. 29. — 5. —17.2 

Pounds per square yard 494 .476 + .018 +3.78 

Pounds per feed, 10 hours 9.74 

Square yards per feed, 10 hours. . . 19.75 
Tensile strength lengthwise 

(of 1 inch strip) 78. 

Tensile strength crosswise 24.35 

Width, 600 needles 17.6 18. — .4 — 2.2 

The calculated results are surprisingly close to the actual 
results. Altho the courses show a 17% variation from the calcu- 



KNITTING CALCULATIONS 7 

lated results and the cut a 10% variation, this is not much 
against the calculations, for the knitter was free to select both 
the cut and the stitch. The other variations, 6% for yarn, 7% 
for wales, 4% for weight of fabric and 2% for width, show 
reliability of calculation comparable to that of industries which 
have attained a high degree of technical development; and 
ought to be sufficient to carry conviction of the dependability 
of knitting calculations. 

(4) The Relations Which Underlie the Calculations 

It may be seen by inspection of a piece of knitting that the 
width of the wale depends to a considerable extent on the thick- 
ness of the yarn ; that four thicknesses lying side by side make 
up the width of the wale. Experimental investigation has shown 
that the length of yarn in the loop — which length decides the 
number of stitches per foot of yarn and the number of courses 
per inch — also depends, altho less definitely, on the thickness 
of the yarn. These relations afford a good basis for calcula- 
tions concerning the dimensions of the fabric. Then, it is 
evident that there must be some relation between the thickness 
of the yarn and the spacing of the needles on which the yarn is 
used. Two folds of an inch rope could not be crowded between 
needles only a quarter of an inch apart, and thread would not 
fill them sufficiently to be usable. Such a range of yarn thick- 
ness is evidently out of the question. Careful investigation 
shows that the general range is much more restricted than the 
range imagined even by knitters. The knitter who brags that 
he can use on his machine yarn twice as heavy as he is 
accustomed to using would generally be sadly embarrassed if 
you required him to make good his boast, and remained to watch 
the operation of the machine. This relation of the yarn to the 
needles affords a very satisfactory basis for the calculation of 
knit-fabric production. All these relations and others are dis- 
cussed in "The Science of Knitting." * 

(5) The Influence of the Yarn Diameter 

But to what extent can we depend on the thickness of the 
yarn ? Let us consider the conditions involved. A yarn, nomin- 



* Procurable from the publishers of this book — price $3.00 



8 KNITTING CALCULATIONS 

ally round, is run into a knitting machine under a certain feed 
tension, is formed into loops, and is drawn off under a certain 
take-up tension. Evidently, it is stretched, compressed, and 
distorted to an extent all through the operation. Whereas the 
cross section was originally circular or approximately so, the 
cross section in the fabric may diverge much from the circular 
form, and may be different in different places in the fabric. 
Let us grant all that. Then let us take a yarn one-fifth larger 
in diameter, and put it through the same operations on the same 
number of needles on a correspondingly coarser gage. There 
is every reason to believe that the fabric would be one-fifth 
wider. Indeed, extensive experimentation shows that when 
the conditions are made as nearly alike as is possible in two 
cases the widths of the fabric are very nearly proportional to 
the original diameters of the yarn. However, we know that 
we cannot exactly duplicate the conditions, so we are warranted 
in expecting that the widths would be exactly proportional to 
the yarn diameters if we could exactly duplicate the conditions. 
Therefore, if we base our calculations on the diameter of the 
yarn, and estimate on the other conditions we will have a fairly 
reliable basis. Moreover, as we progress with our calculations 
we may be able to reduce some of the other conditions to a 
calculation basis, also. For instance, the type of machine seems 
to have an influence on the width of the fabric: certain body 
rib machines make it slightly wider than the calculations call 
for, and certain ribbers (cuff machines, so called) make the 
fabric slightly narrower. The tendency of any machine may be 
determined by observation of the constant difference between the 
calculated width and the actual width when other conditions 
than the yarn diameter are not changed. Indeed, every knitter 
should observe and record the direction and extent of such 
tendencies, for the trade has need of that information. 



(6) Diameter, Diameters, and Coils 

Evidently it is necessary to know the thickness of yarn. 
This thickness is generally designated as diameter ; but since the 
diameter is too small for convenient use, and since the number 
of diameters per inch corresponds better with the units used in 
knitting, the latter or a reduction thereof, (as the diameters per 
half-inch) is preferable. As an illustration of the simplicity 



KNITTING CALCULATIONS 9 

afforded by the use of diameters per inch, they vary in direct 
proportion with the wales, courses, stitches per foot of yarn, and 
cut of machine — four important factors involved; whereas the 
diameter of the yarn varies inversely. That is, when those 
factors increase, the diameter decreases, a relation much less 
comprehensible and convenient than the direct proportion. How- 
ever, in the use of diameters per inch we encounter a language 
difficulty : diameters-per-inch is too cumbersome to say or write, 
and diameters is too readily confused with diameter. The author 
has adopted the term Coils instead of diameters, not only for 
its distinctiveness and shortness, but because it conforms to 
his method of determining yarn size by coiling the yarn on a 
watch-chain bar. For ordinary calculations the diameters per 
half -inch are the most satisfactory, and they are here designated 
Coils per Half-Inch, or i/ 2 Coils. 

(7) How to Get the Coils Per Half-inch 

The Coils per Half-Inch are simply the diameters per half- 
inch; that is, the number of threads, which, lying alongside as 
closely as they do in the fabric, will cover half an inch. There- 
fore, there is nothing mysterious or new about them. They may 
be found by measurement; may be derived by dividing by two 
the diameters tabulated in various textile books; or may be 
calculated from the yarn number in the manner shown later. 
The best procedure is to memorize them. 

(8) Table of Diameters Per Half-inch (Here Called Y 2 
Coils) of Single, Mule-Spun, Carded, Cotton Yarn 

Yarn Number % Coils Yarn Number %. Coils 

4 21 24 51.5 

6 26 26 53 

8 30 28 55.5 

10 33 30 57.5 

12 36 32 59 

14 39 34 61 

16 42 36 63 

18 44.5 38 65 

20 47 40 66 

22 49 



10 KNITTING CALCULATIONS 

(9) The Coils Should be Memorized 

This is not a difficult table to learn, even in its entirety. 
However, most of those concerned with knitting calculations 
would use only a portion of the table. The pros and cons of 
memorizing this table are simple. With the coils the usual 
knitting problems may be solved mentally, or nearly so : with the 
yarn number, square-roots must be used. The time required to 
memorize the table would be spent in solving only a few prob- 
lems by means of the yarn number; so it is far more efficient 
and satisfactory to memorize the table. The reader is not 
restricted to this table. The yarn he uses may be larger or 
smaller; in which case each number of coils is decreased or in- 
creased by a certain proportion. Let him tabulate the yarn 
numbers and whatever coils he may wish; hang the tabulation 
up where he can see it frequently ; and, whenever the yarn num- 
ber comes to mind, think of the corresponding number of coils. 
He will soon come to think of the yarn in terms of its coils, and 
thereafter he will be able to solve many of his problems mentally 
or nearly so. 

(10) Materials 

Altho the principles involved in these calculations apply to 
any material, cotton is the material generally considered, be- 
cause cotton is most used in practice, because the diameter of 
cotton yarn has been determined more extensively than the 
diameter of other yarn, because cotton yarn is readily suscentible 
of measurement, and because the cotton count is probably used 
more extensively than any other yarn count. 

(11) Materials Other Than Cotton 

For materials other than cotton, allowance must be made 
for difference in the size of the yarn — between cotton and that 
material — when there is a difference. For instance when woolen 
yarn is considered, and the cotton equivalent is used, if the 
woolen yarn is thicker, the courses, wales, thicknesses and 
stitches per foot will be less than the formulas give. When the 
yarn diameters for these other materials are determined, the 
constants in the formulas may be modified accordingly. The gen- 
eral production formulas, the general knit fabric formula, and 
those formulas which do not depend on the diameter of the 



KNITTING CALCULATIONS 11 

yarn, hold good for any material when the yarn number is 
transformed to the cotton count. 

(12) Regular Fabrics 
We increase our understanding of things, and our ability 
to communicate that understanding, by classifying them. Knit 
fabric is classified according to the form of the stitch into flat 
fabric, ribbed, warp, etc. ; but it is only very recently that we 
have come to a classification according to the size of the loop 
measured by the diameter of the yarn of which it is formed. 
The basis of this classification is correspondence of character- 
istics, no matter what the size of the yarn ; that is, the relation 
of the strength in each direction, the elasticity in each direction, 
and the number of stitches in each direction is the same. Ex- 
perience shows that fabric with 25% more courses than wales 
represents what is generally considered to be good knitting; so 
the relation of the length of the loop to the diameter of the 
yarn in that fabric has been found, and all fabrics having that 
relation have been called regular, to distinguish them from 
fabrics having more or less yarn in the loop. Complete sets 
of formulas have been derived for these regular fabrics for use 
when we have no other standard of reference. For instance, 
suppose we are asked what is the weight per square yard of 
rib fabric made of number 16 yarn. The formula for that 
weight is (13) 1.808 -~- \/Yarn number — 1.808 -f- yl6 = 
1.808 ~- 4 = .45. That is, one square yard of rib fabric such 
as is generally made of number 16 yarn weighs .45 of a pound. 
However, when we have a weight to figure from, we may use 
other rules, which are also given. The adoption of regular 
fabrics for a standard is not in the least an attempt to exclude 
different fabrics from consideration, but to establish a basis for 
understanding in case we have no other basis. 

(14) Strength of Fabric 
The strength calculations are based on the average of the 
best obtainable tests of soft-twist American yarn. For 

(15) yarn diameter = -q— >r — r- that avera S e is 

2lyNumber 

(16) 600 X (yarn diameter) 2 . The units are pounds and 
inches. Those who use yarn of different strength may modify 
the formulas accordingly. 



12 KNITTING CALCULATIONS 

(17) The Simplicity and Unity of Knitting Calculations 

Knit fabric, as compared with woven fabric, has two 
characteristics of much importance in connection with calcula- 
tions. One of these characteristics is that the yarn is, almost 
without exception, of the same size and character throughout. 
The other characteristic is that, owing to the formation of the 
loop, the wales tend to come close together, so that the width 
of the fabric — for a given number of needles — is determined 
very largely by the diameter of the yarn. Woven fabric is 
generally made with yarns different in size and characteristics 
and the threads per inch, below a certain maximum, are not 
necessarily determined by the size of the yarn. Consequently, 
the calculations applicable to knit fabrics have a simplicity and 
a unity far exceeding those of woven fabrics. 



(18) Choice of Units 

Unfortunately that simplicity of principle is clouded by 
inadequacy of the available units. The yarn number is gener- 
ally usable only as a square or as a square-root; the tabulated 
diameters of yarns are very incomplete, and are theoretical 
diameters instead of those which affect the machine and the 
fabric ; and convenient methods of determining the diameter are 
little understood and less practiced. Naturally there will be 
much opportunity for choice in the selection of the unit for any 
particular case, for there is the double consideration of suit- 
ability for the calculation and availability of the unit. Also, 
the close connection of knitting calculations makes possible 
many transformations from one quantity to another : the stitches 
may be determined from the cut of the machine ; the longitud- 
inal strength may be determined from the wales per inch ; etc. 
The advantage afforded by the very number of these calculations 
is offset by the aversion of the beginner to take up what seems 
to be a stupendous task. It is necessary therefore to impress 
on him that each calculation may be used without learning any 
other, and that a complete set of calculations is available with 
any one unit. It is not necessary to take the whole dose in 
order to get the benefit. Indeed, he may with a very few calcu- 
lations solve all the problems which generally come to him. If 
he desires to go more deeply into the subject he may do so, but 
it is not necessary. 



KNITTING CALCULATIONS 13 

Probably the best way to dispel the apparent confusion is 
to explain in the first place the connection of the customary 
units, so that the user may derive one from any other, according 
to his choice. 

The yarn number is the most available unit. A series 
of measurements of mule-spun carded cotton yarn showed that 
the average diameter was given by the equation 

(19) Yarn diameter = 1 -^ 2lyYarn number, according 
to which 

(20) Yarn diameters per inch = 21 V Yarn number. 

If yarn of different diameter is used the constant, 21, may 
be changed accordingly. 

There is a convenient means of determining the diameter 
of the yarn by coiling it on a wire or on a watch-chain bar 
and making a simple calculation. For the yarns ordinarily 
used, the number of coils per half -inch may be determined with- 
out the calculation, and are much more satisfactory, because 
many of the dimensions of the fabric are directly proportional 
to them and because they are integral instead of fractional. 
Those who do not make the actual determination may derive 
them from the yarn number by the expression 

(21) i/ 2 Coils = 10.5V Yarn number. Evidently, 

(22) Yarn diameter = 1 -=- 2 X V2 Coils. 

The following table of numbers and their square roots 
obviates the necessity of calculating the square roots of the 
yarn numbers. 

Number (23) Square Root Number Square Root 

5 2.236 20 4.472 

6 2.450 21 4.583 

7 2.646 22 4.690 

8 2.828 23 4.796 

9 3. 24 4.899 

10 3.162 25 5. 

11 3.317 26 5.099 

12 3.464 27 5.196 

13 3.606 28 5.292 

14 3.742 29 5.385 

15 3.873 30 5.477 

16 4. 31 5.568 

17 4.123 32 5.657 

18 4.243 33 5.745 

19 4.359 34 5.831 



14 KNITTING CALCULATIONS 

(24) Speed of Machines 

It is customary to run the machines at a fixed needle speed, 
as high as the work will stand without excessive damage and 
waste. Accordingly, small cylinders run fast and large cylinders 
run slow, compared with the average size. Generally a certain 
number of revolutions is adopted for the average size, say a 
20-inch cylinder, which size is convenient as a basis of com- 
parison. (25) The diameter multiplied by the revolutions is 
called the diametral revolutions, and this number is used to 
determine the revolutions of the other sizes. 

Latch-needle rib machines are supposed to run on cotton 
work at about 35 revolutions for a 20-inch cylinder. Then the 
diametral revolutions are 20 X 35 = 700. (26) To find the 
number of revolutions for any other size, divide 700 by that 
size. For instance, the number of revolutions for a 16-inch 
cylinder is 700 -=- 16 = 44. 

Loop-wheel spring-needle machines are supposed to run 
at about 50 revolutions for a 20-inch cylinder; so the diametral 
revolutions are 1,000; (27) and revolutions = 1,000 -^ 
diameter of cylinder. A 24-inch cylinder should run at 1,000 
-r- 24 = 42. 

The above mentioned speed standards are used in the cal- 
culations unless other standards are mentioned. However, 
anyone may use his own standard, according to the exigencies 
of his work. 

(28) Yarn Counts 

There are two yarn numbering systems in general use; 
namely, (1), the length of a standard weight, and, (2), the 
weight of a standard length. 

In the first system, the length is expressed in hanks. For 
instance, number 20 cotton is called number 20 because a length 
of 20 hanks weighs a pound, the standard weight. (29) To find 
the length in yards in one pound, the number of hanks in a 
pound must be multiplied by the length in yards of one hank. 
In this case, the length in yards in a pound is 20 multiplied by 
840, which is 16,800. 

In the second system, the weight is generally expressed in 
grains, and the standard length is generally expressed in yards. 



KNITTING CALCULATIONS 15 

For instance, the Cohoes standard is the weight in grains of 
6% yards. 

The system of numbering yarn by the diameters (coils) 
per inch has been adopted to a considerable extent in weaving 
calculations. It is preeminently useful in knitting calculations, 
so it is used extensively in this series. However, this topic has 
to do with the older systems only, not the diameters (or coils). 

(30) Length-of-a-Standard-Weight System 

Prominent Counts 
Name. Cut (Lea) Run. Cotton. Worsted. Metric. 

Yards in one-pound hank 300 1600 840 560 496 

(1000 meters 
per kilogram) 

Proportional numbers .. 112 21 40 60 67.74 

Transformations within the system may be effected by 
means of the yards in a hank, but more readily by means of the 
proportional numbers. It is evident, that of two counts the one 
with the longer hank has the lower number. The cotton number is 
lower than the worsted number. (31 ) To transform cotton count 
to worsted count we have the proportional numbers 40 and 60, 
and since we are to get a higher number, 60/40 or 3/2 is the 
quantity by which we are to multiply the cotton number to get 
the worsted number. Number 20 cotton multiplied by 60/40 or 3/2 
equals 30, the worsted number. Transformations between any 
two counts in the above table are made in the same manner. 



(32) Weight-of-a-Standard-Length System 

Counts in Use 





Amster- 


New 






Name. Cohoes. 


dam. Canadian. 


Hampshire. 


Silk. 


Denier. 




12% 20 


50 


36.57 


633.9 


Proportional numbers 25 


50 80 


200 


146.28 


2535.6 



The proportional numbers facilitate transformation. Of 
any two counts in this system the one with the greater length 
has the higher number, and this is a guide to the use of the 
proportional numbers. For instance, to transform number 10 
in the Amsterdam standard to the Canadian standard we have 
two proportional numbers, namely, 50 and 80. (33) Since the 



16 KNITTING CALCULATIONS 

Canadian number will be higher than the Amsterdam number, 
we should multiply the latter by 80/50 or 8/5. 10 X 8/5 = 
80/5 = 16, the grains, Canadian, of 10 grain, Amsterdam 
yarn. 

(34) Transformations Between the Two Systems 

To transform between two counts in different systems, a 
number called a constant is used. That number, divided by 
any yarn number in one system, gives the corresponding yarn 
number in the other system. For instance, (35) 625 divided 
by any worsted number gives the corresponding New Hamp- 
shire Number, and vice versa. Constants for all the counts 
mentioned are given in the following table. 



(36) Constants for Transformation Between the Two 

Yarn-Numbering Systems 

Cut (Lea). Run. Cotton. Worsted. Metric 

Cohoes 145.82 27.34 52.08 78.12 88.20 

Amsterdam 291.70 54.68 104.16 156.25 176.40 

Canadian 466.70 87.50 166.70 250. 282.25 

New Hampshire 1166.80 218.72 416.64 625. 705.60 

Silk 853.33 159.37 304.76 457.14 516.31 

Denier 14790. 2770. 5280. 7920. 8950. 

The second yarn numbering system, the weight-of-a-stand- 
ard-length, makes the number increase as the weight of the 
yarn increases, and this is a desirable characteristic; but the 
counts in this system are not in general use, so they are not 
introduced in the calculations. It frequently happens, however, 
as in knitting mills where woolen yarn is spun on mules, that 
all the yarn in the mill is numbered in some count of the weight- 
of-a-standard-length system; so some of the calculations are 
made more readily by using the count in which the yarn comes. 

(37) For two-thread work the sum of the numbers is the 
equivalent number, and (38) the proportion of either thread 
in the fabric (when the stitches are the same) is the number of 
that thread divided by the sum of the numbers of the two 
threads. However, for general fabric calculations, it will be 
found advisable to use the solutions given, as they have been 
selected for their simplicity. 



KNITTING CALCULATIONS 17 

(39) Single Equivalent of Two Yarns 

The single equivalent of two yarns is their product divided 
by their sum. 

(40) Example. What is the single equivalent of a num- 
ber 10 yarn and a number 20 yarn? 

The product of 10 and 20 is 200; the sum of 10 and 20 
is 30; and 200 divided by 30 equals 6.7, the number of the 
single equivalent. 

(41) Example. A manufacturer is making 22-gage 
spring-needle fleeces and is using a number 26 face thread and 
number 26 binder. He hears that a competitor is using for the 
same gage a number 22 face thread and a number 30 binder. 
What are the single equivalents in each case. 



(42) (1) J^_£^L = _^L = 13 



26 X 26 


676 


26 + 26 


52 


22 X 30 


660 



(43) (2) J^fL^^L = _™L = 12.7 

22 + 30 52 

The second combination is slightly heavier than the first. 

Notice that when the two yarns are alike the single equiva- 
lent is half the number; that is, two number 26 yarns are 
equivalent to one number 13. 

(44) Example. A machine is run with 18 cotton and 24 
worsted. What is the single equivalent? 

Number 24 worsted is equivalent to number 16 cotton. 

(45) = = 8.5, the single equivalent. 

18 + 16 34 



(46) Single Equivalent of Three or More Yarns 

The simplest method of obtaining the single equivalent of 
three or more yarns is to find the equivalent of one pair, then 
combine that with the next yarn, and so on until all the yarns 
are combined. There are expressions for the combination of 
any number of yarns ; but they are not readily remembered, and 
are not generally at hand when needed. The expression for 
combining two yarns is so simple that it is readily remembered ; 



18 KNITTING CALCULATIONS 

and since it may be used successively to combine any number of 
yarns, it is preferable to depend on it for all such combinations 
rather than to risk mistakes by endeavoring to keep in mind 
each different expression. 

(47) Example. What is the equivalent of 12, 18, and 36 
yarn? 

Combine the 12 and the 18 yarn. 
12 X 18 216 

(48) 12 + 18 30~ = 7 * 2 

Now combine the 7.2 yarn with the 36. 
7.2 X 36 259.2 
^ 49 ^ 7 2 4- 36 = 43 2 = **' the single e Q uiva lent of 
12, 18 and 36 yarn. 



(50) One of Two Yarns Equivalent to a Third Yarn 

To find one of two yarns equivalent to a third yarn, divide 
the product of the given yarn and the equivalent by their 
difference. 

(51) Example. What number yarn must be combined 
with number 10 to make the equivalent of number 6? 

10 X 6 60 

= 15. 



10 — 6 ~ 4 

(52) Example. Prove the above example. 

The number 10 and number 15 combined should be equiva- 
lent to the number 6. 

10 X 15 150 

10 4- 15 = _ 25~ = 6 * 

(53) Proportions of Yarn in Two-Thread Work — 
Equal Stitches 

The frequency with which two-thread work is knit makes 
it desirable to be able to calculate the proportions of the threads 
in the fabric. The simplest case is that in which the two 



KNITTING CALCULATIONS 19 

yarns are knit with the same stitch, which is generally the case 
when both yarns are drawn into the machine with the same 
feeding device, as with a latch needle or with a single loop- 
wheel. The case is not so simple when a separate feeding 
device is used with a separate stitch for each thread, as in the 
knitting of flat fleeces, or two-thread work with two sinkers 
at a feed. 

When the stitches for each yarn are alike the yarn numbers 
are the only factors involved. They should be expressed in the 
same yarn count, preferably the cotton count, altho one of 
them will probably be worsted or possibly silk. 

(54) The proportion of one yarn in the fabric is the 
number of the other yarn divided by the sum of the numbers 
of the two yarns. 

(55) Example. A two-thread fabric is knit of number 16 
and number 24 yarn. What is the proportion of each in the 
fabric? 

To find the proportion of number 24 yarn divide the num- 
ber of the other yarn, namely, 16, by the sum of the numbers 
of the two yarns, which sum is 40. 16 -=- 40 = .40. Then 
the proportion of 16 yarn would be .60; but solve for the 
proportion of 16 yarn in order to prove the work. 24 -^ 
(16 + 24) = 24 -^ 40 = .60. Since the yarn number is an 
inverse measure of the weight of the yarn, it is evident from 
inspection in this case that there will be half as much more 
of one yarn than the other and that there will be the greater 
weight of the lower number. 



(56) Proportions of Yarn in Two-Thread Work — 
Unequal Stitches 

When the stitches are equal the proportion of either thread 
in the fabric is the number of the other thread divided by the 
sum of the numbers of the two threads. 

Consider two yarns of the same size but knit with unequal 
stitches as in the case of plated work, in which the face thread 
is preferably knit with less stitches per foot of yarn in order 
to make the face loop longer than the loop on the back. Since 
an increase in the stitches per foot of yarn causes a decrease 



20 KNITTING CALCULATIONS 

in the amount of yarn used, the proportion of either yarn in the 
fabric would be the stitches per foot of the other yarn divided 
by the sum of the stitches of the two yarns. In other words, 
the stitches have the same inverse effect on the proportions that 
the yarn does. 

Consequently, (57) for two-thread work in which both 
the yarns and the stitches are different, the proportion of either 
yarn in the fabric is the product of the other yarn and stitches 
divided by the sum of the products of each yarn and its stitches. 
That is, multiply together each yarn and its stitches, and divide 
one product by the sum of the two products : the quotient is the 
proportion of the other yarn. 

(58) Example. A 9-pound (to the dozen of men f s gar- 
ments), 20 gage, plated fabric is made of number 30 worsted 
at 57 stitches per foot of yarn and number 14 cotton at 63 
stitches. What is the proportion of wool and cotton in the 
fabric? 

Reduce the worsted number to the cotton number. 

(Worsted number) (Reduction factor) (Cotton number) 
(59) 30 X 2/3 = 20 

qtii^hoa Products of r>r.™Qin> Proportions 

Thread Number „l l r tc f „® s stitches and " PP >° 'Jf Total (Opposite products 

per foot num bers products divided by total) 

Back 14 63 882 1140 \ f .564 

Face 20 57 1140 882 J 2022 I .436 



Total 2022 1.000 

The fabric is 44% wool and 56% cotton. 

(60) Gage and Cut 

The gage and the cut are each the number of needles per 
unit of length. 

(61) Cut is the number of needles per inch of needle line. 
It is applied generally to needle beds which are milled or cut, 
such as those of latch-needle machines. When interlocking sets 
of needles are used, as in rib machinery, the cut of only one 
needle bed — generally the cylinder — is considered. 

(62) The old original knitting gage is the number of 
needles per inch-and-one-half. It was expressed as the number 



KNITTING CALCULATIONS 21 

of two-needle leads in three inches, because the needles 
were leaded in pairs; but that is the same as the number of 
needles per inch-and-one-half. 

There are hybrid gages, such as the number of needles per 
two-inches; but these are as undesirable as the original gage, 
and lack even the justification of well-established use. In the 
interest of simplicity it seems desirable that needles-per-inch, 
even when the number is fractional, be used to displace gage 
as a standard for the needle spacing of machines. 

Gage is also used to indicate the thickness of latch needles. 
Whatever significance it may have had as a standard has been 
lost, and it is now principally a source of confusion and vexa- 
tion. The tendency is to substitute the word "thickness" for 
it, and to express the thickness in thousandths of an inch. 

The original knitting gage has deteriorated in its applica- 
tion to circular machines through measurement outside of the 
needle line, or on the chord, or other defective measurement. 
Similar errors have crept into standard cuts, also. In these 
calculations such errors will be neglected. Whoever desires to 
reckon with them may obtain the exact number of needles per 
inch from the maker of the machines in question. 



(63) Example. A spring-needle machine is 14 gage. 
What cut is it? 

Cut is the needles per inch, and gage is the number of 
needles per inch-and-one-half. Therefore the cut of the spring- 
needle machine is, 

14 -j- 1.5 = 9.33 



(64) Example. A visitor to a latch-needle mill asks the 
knitter what the gage of the machines is. They are 8-cut. How 
shall the knitter answer intelligently? 

Since machine gage is the number of needles in an inch- 
and-a-half, and cut is the number of needles in an inch, it is 
merely necessary to tell the number of needles in an-inch-and- 
a-half, which is of course V£ more than 8, namely 12. 



22 KNITTING CALCULATIONS 

(65) Example. A machine is 20 inches in diameter and 
contains 500 needles. What is the cut? 

The length of the needle line is 20 X — = 20 X 22 an d 
500 divided by the length of the needle line is 

500 X 7 



20 X 22 



= 8, nearly. 



(66) Example. A spring-needle, loop-wheel machine 20 
inches in diameter contains 988 needles. What is the gage? 

Solve for the cut, and then increase the cut by 50% to get 

22 

the gage. The length of the needle line is 20 X — and 988 

7 

988 X 7 

divided by the length of the needle line is == 15.72. 

20 X 22 

Half of 15.72 is 7.86; which, added to 15.72 is 23.58. The 
machine is nominally 24 gage. The difference between the 
actual and nominal gages gives a fair idea of the discrepancy 
frequently found in practice. 



(67) Yarn and Cut of Machine 

Probably the best conception of the relation of the yarn 
to the cut of the machine is obtained by imagining pieces of 
the yarn laid alongside, and a needle laid on every 5th, 6th or 
7th needle, according to the type of machine in question. For 
a straight, jack-sinker, spring-needle machine the needles would 
be spaced 4 1/5 threads ; for a latch-needle hosiery machine or 
a spring-needle loop-wheel machine about 5 threads; for a 
circular spring-needle rib machine about 6 2/3 threads ; for a 
latch-needle rib machine about 8 1/2 threads. Then, whatever 
the size of the thread, the needle spacing would correspond, for 
the distance between the needles would be proportional to the 
size of the yarn. We could take the diameter of the yarn and 
multiply it by 4 1/5, 5, 6 2/3, 8 1/2 — according to the type of 
machine under consideration, and obtain the needle spacing. 
But, instead of using the needle spacing in practice, we use the 
number of needles in a certain space — an inch, or an inch-and- 



KNITTING CALCULATIONS 23 

a-half — and that number decreases as the diameter of the yarn 
increases, so the diameter would have to be used as an inverse 
proportion. To obtain a direct proportion the diameters per 
inch, or preferably the coils per half-inch, may be used, for 
both they and the cut increase, or decrease, together. The coils 
per half-inch would be divided by half of the above numbers to 
obtain the cut. If the reader uses a machine not in the above 
list, or if he prefers a different proportion than the one given 
for any machine in the list, he has merely to divide the coils 
per half -inch by half the cut in order to get the number, which 
should hold for all other cuts of that type of machine. For 
instance, suppose he uses number 8 yarn on a 10-cut latch- 
needle machine for making flat work. Approximately 60 diam- 
eters of the yarn make up one inch; and ten of the needles 
occupy an inch ; so there are 6 diameters of yarn to one needle. 
Consequently, if we divide the diameters per inch by 6, or the 
diameters (coils) per half -inch by 3, we get the cut. 

Coarse machines, say 5-cut latch-needle rib, and 10-gage 
loop-wheel machines and coarser, will not take as heavy yarn 
as average-gage machines, because they are not as well designed 
as the average-gage machines. Special constants may be used 
for these coarse machines. 



(68) Example. A yarn coils 43 turns per half-inch 
(about number 17). What is a suitable cut for rib work? 

(69) Cut = V 2 Coils -=- 4.3, = 43 -j- 4.3 =10. 

(70) Example. The diameter of a yarn is .01 (about 
number 23). What is a suitable cut for latch-needle, rib work? 

(71) Cut = 1 -r- Diameter X 8.6 

= 1 -=- .01 X 8.6 

= 1 -=- .086 

= 11.6 say 12 cut. 

(72) Example. A latch-needle rib machine with external 
dial runs satisfactorily on 11 cut with two-thread combina- 



24 KNITTING CALCULATIONS 

tions equivalent respectively to 8.5 and 6.86. What is the 
Yarn-Cut formula for this machine. 

(Cut) 2 (Cut)' 

(73) Yarn = (74) Constant = 



Constant. Yarn 

r m 
(75) 



f (1) 121 -r- 8.5 = 14.3 
"| (2) 121 -f- 6.86 — 17.7 

The total of 14.3 and 17.7 is 32; the average is 16; so 

the Yarn-Cut formula for this type of machine for a two-thread 

(Cut)' 
equivalent is (76) Yarn = 

Fortunately the yarn number may be determined from the 
cut without much trouble; and this is one of the frequent 
applications of the relation. 

(77) Example. A mill is equipped with 8-cut rib machines 
of the usual type. What is a good yarn to use? 

(78) Yarn = Cut X Cut -v- 6 
= 8x8^-6 
= 64-^-6 
= 10.7, say 11 

(79) Example. A straight, jack-sinker, spring-needle 
machine, 25 gage, runs satisfactorily on woolen yarn equivalent 
to 11.4 cotton number. What is the yarn formula for this 
machine for corresponding running conditions? 



(80) Yarn = Cut X Cut -f- A constant. 


Therefore, 


(81) The constant = Cut X Cut -f- Yarn 




= 25 X 25 -f- 11.4 




= 625 -~ 11.4 




= 55. 





The yarn rule for this machine is 

(82) Yarn = Cut X Cut ~ 55. 

(83) Example. A mill is running number 16 yarn (42 
coils to the half -inch) on 24 gage loop-wheel machines. It is 



KNITTING CALCULATIONS 25 

contemplated to add both latch-needle and spring-needle rib 
machines. What would be appropriate cuts for the same yarn? 

Latch. (84) Cut = i/ 2 Coils -*- 4.29 = 
(85) 42 -r- 4.29 = 10 

Spring-needle. (86) Cut = i/ 2 Coils -f- 3.32 = 
(87) 42 -f- 3.32 = 12.7 

(88) Wales 

(89) Example. A yarn is .01 inch in diameter (about 
number 23). What will be the width of the wale made of it? 

The width of the wale is made up of four thicknesses of 
yarn, therefore, 

.01 x 4 = Width of wale — .04 

(90) Example. A yarn is .015 inch diameter (about 
number 10). How many wales per inch will there be in the 
fabric made of it? 

The width of the wale will be (91) .015 X 4 = .06, and 
the number of wales per inch will be 1 -f- .06 = 16.7. 

(92) Example. How many wales per inch will there be in 
fabric made of number 16 yarn? 

1 

(93) Diameter of yarn is approximately 

21 V Yarn number 

So the diameter of No. 16 yarn is 

111 

= .0119 



21V16 21 X 4 84 

(94) The width of the wale is 4 times the diameter, or 

1 1 

4 X — = and the wales per inch are 1^- (the width of the 

84 21 

1 

wale), 1 -f- — =21 wales per inch. 
21 

(95) Example. A body rib machine makes fabric 10% 
wider than would be expected from the diameter of the yarn. 
How many wales per inch will the fabric have when yarn .013 



26 KNITTING CALCULATIONS 

inch in diameter is used (about number 13). The normal 
number of wales per inch would be (96) 1 -f- (4 times the 

diameter of the yarn), or 1 -f 4 X .013 = - - = 19.2. But 

.052 

in this machine these 19.2 wales will cover 1.1 inches, because 

this machine makes the fabric 10% wider than would be 

expected. To find the wales per inch divide 19.2 by 1.1 and 

the wales per inch are 17.5. 

(97) Example. A yarn coils 21 turns per half -inch 
(about number 4). How many wales should be expected in the 
fabric made of it? 

(98) Wales = i/ 2 Coils -r- 2 — 21 -j- 2 — 10.5 



(99) Width of Fabric 

The principal factors which affect the width of the fabric 
are the diameter of the yarn in it and the number of needles in 
the machine on which it was knit. Since most fabric is tubular, 
and the width is consequently considered to be the width of the 
flattened tube, only half the needles in the cylinder are effective 
in producing that width. 

Among the less important factors which affect the width 
of the fabric are the elasticity of the yarn, the tension under 
which the yarn is fed and the fabric rolled, the subsequent 
treatment, such as washing, drying, steaming, etc. These 
factors have not been investigated with sufficient thoroughness 
to facilitate calculations concerning them; so allowance must be 
made for them. The calculations apply to the widths delivered 
by the machine. 

Each needle makes a wale, and a wale is four diameters of 
yarn in width; so the width of the fabric is four times the 
diameter of the yarn multiplied by the effective number of 
needles. 

(100) Allowances, not always made here, may be 10% 
less than the calculated width for ribbers, loop-wheel, and single- 
set latch-needle machines, and 10% more for body rib machines. 

(101) Example. A machine has 500 needles in the 
cylinder and is knitting yarn .015 inch in diameter (about 



KNITTING CALCULATIONS 27 

number 10 yarn). What theoretical width of fabric is to be 
expected? 4 (diameters in wale) X -015 (diameter) X 250 
(1/2 needles) =15, the theoretical width in inches of the fabric 
to be expected. 

(102) Example. How many needles are needed in a 
cylinder to make fabric 14 inches wide (theoretical) with yarn 
.018 inches in diameter (about number 7 yarn) ? 

(103) The width of a wale is .018 X 4 = .072 

(104) The effective number of needles is 14 -— .072 = 194 
The whole number of needles is 194 X 2 = 388 

(105) Example. A latch-needle cylinder 4 inches in diam- 
eter and containing 175 needles is to be used for making tubular 
bandages with yarn coiling 45 turns per half -inch (about 
number 18 yarn). How wide will the uncut bandage be? 

(Needles) (1/2 Coils) (Width) 

175 -J- 45 — 3.89 

The actual width proved to be 4 inches. 

(106) Example. A circular machine has 400 needles. 
What theoretical width of fabric may be expected with number 
16 yarn? 

(107) The diameter of 16 yarn is 

1 111 



2iy Number 21\/16 21 X 4 84 



.0119 



(108) The width of the fabric = 4 X Dia. of yarn X V2 
needles 

1 , 400 200 

= 4 X M X ~Y = ~^ = 9 ' 5 

(109) Example. What difference in the width of the 
fabric will be made by changing from number 20 yarn to 
number 24 yarn? 

(110) 1/2 Coils for number 20 yarn = 10.5 V20 = 10.5 
X 4.47 = 46.93. 

(111) 1/2 Coils for number 24 yarn = 10.5 V24 = 10.5 
X4.9 = 51.45. 



28 KNITTING CALCULATIONS 

Since the thickness of the yarn decreases as the number 
of coils increases the width of the fabric will be inversely as 
the number of coils. That is, the widths with 20 yarn and 24 
yarn will be as 51.4 is to 46.93, respectively. For convenience 
consider the coils to be 51 and 47. 47 -r- 51 = .92. Therefore, 
the fabric will be approximately 8% narrower with the 24 yarn 
than with the 20 yarn. 

Notice that when, as in this case, the calculation applies 
to relative widths on any one machine the variation due to the 
machine itself is eliminated. The case is different when we do 
not use relative widths. For instance 

(112) Example. What are the specifications for a 
machine to make rib fabric 16 inches in width (of flattened 
tube) with number 14 yarn? 

(113) Since a body rib machine generally makes the fabric 
10% wider than the theoretical width, divide 16 by 1.1 to get 
the theoretical width. 16 -~ 1.1 = 14.5 

(114) The number of needles = Width of fabric X 
i/ 2 Coils. 

(115) V2 Coils — 10.5yYarn number = 10.5yl4 — 
10.5 X 3.74 — 39.27. 

(Width) (i/ 2 Coils) (Needles) 

(116) 14.5 X 39.27 = 570 

(117) Cut — 1/2 Coils -i- 4.29 = 39 -f- 4.29 = 9.1, 
say 9 cut. 



(118) Thickness of Fabric 

The thickness of flat fabric is two diameters of the yarn 
of which it is composed, and the thickness of rib fabric is four 
diameters. A convenient conception of the thickness is obtained 
by the recollection that rib fabric is as thick as one wale is 
wide, and flat fabric is half that thickness. Generally it is more 
desirable to use the thicknesses per inch than the thickness of 
a single piece of cloth. In that case it should be remembered 
that, for rib fabric, as many thicknesses will occupy an inch as 
there are wales per inch. For flat fabric, twice as many thick- 
nesses will be required. 



KNITTING CALCULATIONS 29 

(119) Example. A cutting table is piled 1 foot high with 
rib fabric made from number 28 yarn. How many thicknesses 
of fabric are there in the pile ? 

Number 28 yarn coils about 56 turns to the half -inch; and 
the number of thicknesses per inch is half the number of 
coils or 28. So in twelve inches there will be 12 times 28 
thicknesses, or 336. 

(120) Example. Five inches depth of fabric is the limit 
for a cloth cutter. How many thicknesses of 28 gage balbriggan 
(flat- work) made from number 20 yarn will it cut? 

The number of thicknesses per inch is the same as the 
number of coils per half-inch. 

(121) i/ 2 Coils = 10.5yYarn number = 10.5V20 = 10.5 
X 4.47 = 47. The number of thicknesses in 5 inches = 5 X 47 
= 235. 

(122) Example. A roll of rib cloth is 23V2 inches in 
diameter. The yarn coils 54 turns in half an inch (about 
number 26). How many layers of the tube of fabric are there 
on the roll? 

Since we have no idea of the compression, figure without 
that. (123) The single thicknesses per inch of the fabric are 
i/ 2 Coils -f- 2. (124) The double thicknesses are i/ 2 Coils -^- 4 
= 54 -^ 4 = 13.5. The radius of the roll is 23i/ 2 -s- 2 — 11.75. 
The number of layers is 13.5 X 11.75 = 158.5. A count 
showed the number of layers to be 179; that is 20, or 12Vfc% 
more than the result of the calculation. 



(125) Courses Per Inch 

If the knitter is told that the courses per inch are closely 
related to the wales per inch, and therefore to the diameter of 
the yarn, he is likely to bristle up and challenge the statement, on 
the ground that he can adjust his machine to run almost any 
number of courses that he chooses. But if we ask him whether 
he has ever looked for a relation between the courses and wales, 
he is likely to answer that he never thought of such a thing, 
and that he does not see what good it would do, anyway. If 
we can induce him to put down in two columns side by side the 



30 KNITTING CALCULATIONS 

courses and wales of the goods he is required to make, the 
relation of one to the other will be evident at a glance. The 
number of courses will be between one and two times the number 
of wales in almost any case, and in a large proportion of cases 
the number of courses will run between 1, and 1.5-times the 
number of wales, generally 1.25. Then how about that wide 
range of stitch adjustment? Why the range is there just the 
same, but any fabric made outside of the limits mentioned 
would not be considered good knitting. The long-stitch fabric 
would be shapeless and stringy, and the short-stitch fabric would 
be stiff. That is, for any one yarn, usage has limited the range 
of courses to much less than the machine is prepared to make, 
and to considerably less than we have generally imagined was 
made. One who does not have access to machines in operation 
may use for his calculation (126) courses equals 1.25-times 
wales. Those who have access to the machines in operation or to 
a line of knit fabric may find their ratio by observation. 

(127) Example. How many courses per inch may be 
expected in fabric made of number 25 yarn? 

i 

(128) The yarn diameter == 



2iyNo 

1 

21V25 

1 

21 X 5 
1 



105 



(129) The wales are 4 times the diameter in width 

4 105 

so the number of wales per inch = = 26.25. 



105; 



(130) The courses are generally 1.25 times the wales, 
so the courses = 26.25 X 1.25 — 33. 

(131) Example. A yarn coils 42 turns to the half-inch 
(about number 16). How many courses may be expected in the 
fabric made from the yarn? 



KNITTING CALCULATIONS 31 

(132) The coils per inch divided by 4 equal the wales per 
inch; so (133) the coils per one-half inch divided by 2 equal 
the wales per inch, = 42 -f- 2 = 21. The (134) courses per 
inch may be expected to be between 1 and 1.5-times the wales, 
probably 1.25-times; so the courses to be expected are between 
21 and 32, and probably 26. 

(135) Example. A yarn coils 44 turns to the half -inch 
(about number 18). What is the highest number of courses to 
be expected? 

(136) The number of wales is the number of coils per half- 
inch divided by 2, and (137) the highest number of courses is 
2-times the number of wales; so 44 is the highest number of 
courses to be expected. 

(138) Example. A mill is running number 9 yarn, and is 
reported to be making fabric with 14 courses per inch. Is the 
mill making good fabric? 

(139) The yarn diameter is 

1 111 



2iyNo 2ly9 21 X 3 63 

(140) The number of diameters per inch is 1 -f- the 
diameter, or 63. (141) The number of wales is *4 of the 
diameters per inch, and (142) the number of courses for what 
is considered good fabric is 1.25-times the wales ; so 63 X 1-25 
-r- 4 = the number of courses to be used as a criterion = 20. 

(143) Fabric which is considered sleazy has the same number 
of courses as wales; which number, in this case, is 63 -f- 4 
= 16. Since 14 courses is less than either of these — far less 
than 20, and even less than 16, considered to be the limit for 
looseness — the fabric cannot be pronounced good. 

(144) Example. A government specification calls for 
fabric having 18 courses and 28 wales. Is the specification 
reasonable, and if so what will be the character of the fabric? 

Courses divided by wales = 28 -f- 18 = 1.56. The specifi- 
cation is reasonable, since the limit of the ratio is approxi- 
mately 2. The fabric is on the heavy side, for a ratio of 1.25 
represents good average practice. 



32 KNITTING CALCULATIONS 

(145) Stitches Per Foot of Yarn 

Consider a piece of hosiery yarn by itself, and it is difficult 
to conceive of a definite number of stitches in connection with 
it. Indeed, one is apt to say, "Why, we can use it with almost 
any number of stitches." But we begin to change our opinion 
on that subject when we consider the same piece of yarn in 
connection with a machine in operation. Submit that yarn to a 
knitter who is running a slightly heavier yarn, and he will say, 
"Why, yes; I can probably run that yarn on my machines by 
tightening the stitch." He knows by experience that since the 
yarn is lighter than what he is running he must tighten the 
stitch; that is, he must make each loop shorter, and thereby 
make more stitches per foot of yarn. In other words, in the 
actual use of the yarn he realizes that as the diameter of the 
yarn decreases the number of stitches per foot must increase; 
but he almost never appreciates the dependability of that rule. 
Indeed, one who has not investigated the subject is not in a 
position to appreciate it; for seeing is believing. Some one 
will say, "But the rule cannot be dependable for I can change 
the stitch to a considerable extent with any one yarn and still 
make satisfactory fabric." Yes, but each fabric will have 
different characteristics, and for any one yarn there is a certain 
stitch which will give those characteristics. Now what is more 
important for advancement than the ability to duplicate a per- 
formance. The steel maker who made every lot of steel differ- 
ent would have to go out of business; on the contrary, ability 
to duplicate what he had made would be an important reason 
for keeping him in business. He might make many different 
grades of steel; but he should be able to duplicate any one of 
them. And how could he do it, if not by duplicating every con- 
dition involved in the process? Is there any principle better 
fixed than the necessity of duplicating the influencing conditions 
in order to duplicate results? Therefore, it ought to be evident 
that, for any particular characteristic of knit fabric, the stitches 
per foot of yarn are closely related to the diameter of the yarn. 
The knitter may determine that relation for each different kind 
of fabric which he makes, and thereafter he has a dependable 
rule for the duplication of the fabric, as far as the stitches per 
foot of yarn are involved. 

But how do we know that the rule holds for yarns which 
differ considerably in diameter? By observation. If one yarn 



KNITTING CALCULATIONS 33 

has a certain number of stitches, the yarn twice the diameter 
will have half the number of stitches for fabric of the same 
characteristics as the first fabric. Possibly, more refined obser- 
vations will show some variation from this rule, but there is no 
indication of sufficient variation to disturb its usefulness. 

Since the stitches per foot of yarn increase as the yarn 
becomes finer, it is evident that the diameters of yarn per inch, 
or coils per half -inch, are more convenient units of reference 
than the diameter of the yarn, both because the relation is direct 
instead of inverse, and because the diameter is too small for 
convenient computation. 

(146) Example. A yarn which coils 35 turns to the half- 
inch (about number 11) is run on a ribber at 33 stitches per 
foot of yarn. At what number of stitches should a yarn be 
run which coils 47 turns per half-inch (about number 20) ? 

The number of stitches is proportional to the number of 

47 
coils, so 33 X — = the required number of stitches = 44. 

35 

(147) It will be noticed that the number of stitches is only 
a little less than the number of coils per half-inch; so for 
slightly heavier fabric, the number of stitches may be made the 
same as the number of coils per half -inch. This is a convenient 
relation to remember. 

A good rule for rib fabric is, (148) Stitches per foot = 
1/2 Coils -~- 1.07. The fabric will have 25% more courses than 
wales. 

(149) Example. A yarn coils 42 turns per half -inch 
(about number 16). What stitch is suitable for rib work? 
42 -f- 1.07 — 39. 

On rib machines the stitches are counted on only one set 
of needles, so half of the stitches are left uncounted. Conse- 
quently, for any one yarn, the number of stitches per foot is 
twice as much for flat work as for rib work. There is no 
difference in the appearance of the face of the goods provided 
the rib fabric is properly made. The flat-fabric rule correspond- 
ing to the one just given is 

(150) Stitches per foot = l/ 2 Coils -?- .54. 

(151) Example. A yarn coils 42 turns per half-inch 
(about number 16). What stitch is suitable for flat work? 
42 -f- .54 == 78. 



34 KNITTING CALCULATIONS 

(152) Example. A yarn .015 inch in diameter (about 
number 10) is used for making flat fabric with 62 stitches per 
foot of yarn. How many stitches should be used with a yarn 
.011 inch in diameter (about number 18) ? 

Since the smaller yarn will have the larger number of 
stitches, we multiply the given number of stitches by the 
diameter of the larger yarn and divide that product by the 
smaller diameter. 

62 X .015 -f- .011 = 85. 

In these calculations involving reduction from a given 
number of stitches, the actual diameter of the yarn is not 
necessary but relative diameters are sufficient. For instance, 
diameters by the specific-gravity method may be used. But 
when the number of stitches is to be derived from the diameter 
of the yarn, then the actual diameter is necessary for depend- 
able results. For instance: 

(153) Example. The diameter of a yarn is .01 inch (about 
number 23). At what number of stitches will it run well for 
flat work? A good rule is 



(154) Stitches = 1 
= 1 
= 1 



1.07 X Diameter 
1.07 X .01 
.0107 



= 94, The number of stitches for flat work. 

When the stitches per foot for rib fabric are to be deter- 
mined from the diameter of the yarn, the method is the same as 
for flat fabric, but the constant is different, because we count 
the stitches on one set of needles only. The number of stitches 
for flat fabric may be derived and divided by 2, or the formula 
for rib fabric may be used, namely, 

(155) Stitches = 1 -f- 2.14 X Diameter. 

(156) Example. Take the same yarn as in the above 
example, namely .01 inch in diameter (about number 23). 
What number of stitches will be satisfactory for rib work? 

Stitches = 1^- 2.14 X .01 
= 1-f- .0214 
= 47, The number of stitches for rib work. 



KNITTING CALCULATIONS 35 

The least convenient means of determining the stitches is 
by the number of the yarn. A good formula for rib fabric is 

(157) Stitches = 9.8V Yarn number. 

(158) Example. What is a good number of stitches per 
foot for rib work for number 25 yarn? 

Stitches = 9.8 V 25 
= 9.8 X 5 
= 49 

For flat work, the constant is 20, instead of 9.8. 

(159) Example. What is a good number of stitches per 
foot for flat work for number 16 yarn. 

Stitches = 20 V 16 
= 20 X 4 
= 80 



(160) Weight Per Square Yard for Change of Yarn and 
Proportional Change of Stitch 

When the stitch conforms to the size of the yarn the 
weight variation is inversely as the coils, and (161) the 
weight in pounds per square yard of rib fabric is about 19-^- 
V2 Coils : the weight of flat fabric is half that. 

(162) Example. A yarn coils 51 turns to the half -inch 
(about number 24). What is the weight per square yard of 
rib fabric made of it? 

19 -f- 51 — .373 

(163) Example. What is the weight per square yard of 
rib fabric made of number 16 yarn? 

In this case it is convenient to solve by means of the yarn 
number instead of the coils for 16 has a simple square root. 

(164) Weight = 1.8 h- VYarn number = 1.8 -f- V16 
= 1.8 -=- 4 = .45 

(165) Example. What is the number of yards per pound 
of rib webbing IV2 inches wide made of number 14 yarn? 

(166) 1/2 Coils = 10.5VYarn number = 10.5V14 = 
10.5 X 3.74 = 39.27. 



36 KNITTING CALCULATIONS 

The weight formula transformed gives (167) the number 
of yards per pound of strips one inch wide = 14 Coils X 1.9. 
Consequently (168) the yards per pound for strips of other 

1/2 Coils X 1.9 

width are In this case 

Width of strip in inches. 

39.27 X 1.9 

(169) Yards per pound = — — = 49.7. 

1.5 

A carefully conducted test gave 50 yards per pound. 

(170) Example. What is the weight per square yard of 
flat fabric made of number 28 yarn? 

For 28 yarn the number of coils per half inch is 56. 

(171) Weight per square yard = 9.5 h- V2 Coils — 9.5 
-f- 56 = .17. 



(172) Weight Per Square Yard for Change of Yarn 
Without Change of Stitch 

It is customary to change the stitch when the number of 
the yarn is changed ; but occasionally the yarn number is changed 
without change in stitch. In that case, for finer yarn both the 
number of courses per inch and the weight per square yard is 
decreased, and for coarser yarn both these quantities are in- 
creased. The change in the weight is inversely proportional to 
the yarn number. 

(173) Example. A manufacturer has been running num- 
ber 10 yarn. He finds that some of his machines were sup- 
plied with number 11 yarn by mistake. What effect will that 
have on the weight per square yard of the goods made by those 
machines? 

The weight of the new goods will be to the old, as the old 
yarn is to the new. The old yarn is 10 and the new yarn is 11. 
10 -f- 11 — .91. The fabric is 9% scant in weight. 

(174) Example. Goods made of number 12 yarn are 
supposed to be kept within 5% either way of the weight per 



KNITTING CALCULATIONS 37 

yard. If all other conditions remain constant, how much varia- 
tion is allowable in the yarn number? 

The allowable weight may be 95% or 105% of the specified 
weight. Therefore, the allowable range in yarn sizes will be 
12 divided by each of these proportions. 

12 ~ .95 — 12.6 
12 -f- 1.05 = 11.4 

The allowable variation is approximately half a count either 
way. 

(175) Strength of Fabric 

The strength of the fabric for one kind of yarn depends on 
the number of threads that stand the stress and the size of the 
threads. Since the wales tend to come together, and since the 
number of wales depends on the size of the yarn, the number 
of threads that stand the lengthwise stress is determined prac- 
tically altogether by the size of the yarn. The crosswise 
strength, however, involves the number of courses, which in 
turn depends on the number of stitches per foot of yarn, and 
this number is variable to an extent. However, for commercial 
knit goods the proportion of courses to wales of 5 to 4, on 
which the formulas are based, gives satisfactory results. For 
special fabrics the reader may derive his own formulas. Since 
fabric does not present definite breaking areas, we cannot 
express the strength per unit of area, so the strength is 
expressed for a unit of width, namely for a strip one inch 
wide. For longitudinal strength the strip is cut along the 
wales, and for transverse strength it is cut along the courses. 

The proportional longitudinal and transverse strength of the 
fabric is seen by inspection. Take the case of fabric in which the 
courses are to wales as 5 is to 4. In flat fabric two threads 
stand the stress in each wale, whereas in nearly any case there 
is only one thread per course (multiple-thread work excluded). 
Multiplying the wales by 2 to get the relative strength, we have 
for (176) flat fabric, longitudinal strength is to transverse 
strength as 8 is to 5. For rib fabric we have to multiply the 
wales by 2 again in order to account for the loops on the back, 
so (177) for rib fabric the relative strength is as 16 is to 5. 



38 KNITTING CALCULATIONS 

Consequently, the two fabrics have the same strength crosswise, 
but the rib fabric is twice as strong lengthwise as the flat fabric. 

(178) Example. What is the strength of rib fabric made 
of number 16 cotton yarn? 

Solve first with the yarn number, since the square root of 
16, namely 4, is extracted by inspection. 

(179) Longitudinal strength = 286 -f- yYarn number = 
286 -r- V16 = 286 -r- 4 = 71 V 2 lbs per inch of width. 

(180) Transverse strength = 89 -^- yYarn number = 

89 -T- yl6 = 89 -j- 4 — 2214 lbs. per inch of width. 

Solve now by means of the coils per half -inch, which are 
42 for 16 yarn. 

(181) Longitudinal strength — 3000 -f- i/ 2 Coils = 3000 

-~ 42 — 71i/ 2 . 

(182) Transverse strength = 938 -j- i/ 2 Coils = 938 

— 42 = 2214. 

It is frequently desirable to know what size of yarn is 
necessary to make fabric of a specified strength. 

(183) Example. What size yarn is necessary to make rib 
fabric having tensile strength of 70 pounds, per inch of width, 
along the wales? 



(184) Yarn number = 81,625 
= 81,625 



(Tensile strength) 1 
70 X 70 



— 81,625 -f- 4900 

= 16.65 Say, 16 yarn. 



(185) Production of Knitting Machines 

The production is generally given in pounds, altho it is 
sometimes given in linear yards, square yards, and in dozens 
or dozen pairs of the articles manufactured. When the unit 
is dozens, the description of the article must be given, for it 
makes considerable difference whether the article is for adults 
or children. 

The production in pounds is found by ascertaining the 
weight in pounds of the length of yarn consumed by the 



KNITTING CALCULATIONS 39 

machine. The machine in question, according to its diameter, 
revolutions, feeds, cut, and stitches per foot of yarn, draws in 
a certain length of yarn. Find what that length is, and its 
weight in pounds is the production. Altho the problem is 
simple, it contains so many factors, that one may become con- 
fused unless each factor is taken at a time. That method is 
followed here. Then all the factors are combined. 



(186) Cylinder Diameter and Pounds Production 

(187) Example. A 14-inch cylinder knits 30 pounds of 
fabric in a day. How many pounds will be knit by an 18-inch 
cylinder running at the same number of revolutions per minute ? 

When other conditions are the same, the production is 
proportional to the diameters of the machines. In this case 

18 
the proportion of the diameters is — , and the production of 

14 

1Q 

the 18-inch cylinder = 30 X - = 38.6. 

14 

(188) Example. A 16-inch cylinder makes the goods too 
narrow. It is proposed to use a 17-inch cylinder, and to run 
it at the same number of revolutions. What will be the change 
in production? 

Since the proposed cylinder is larger than the one in use, 
the change will be an increase, and the amount of the increase 
will be in proportion to the cylinder sizes, namely as 17 : 16. 
17 -r- 16 = 1.06. The increase in production will be 6%. 

(190) Example. A mill making piece goods is running 
40 cylinders 26 inches in diameter. In case 30-inch cylinders 
were used and run at the same number of revolutions, how 
many 30-inch cylinders would be required to keep up the 
production ? 

The increase in the production would be as 30 : 26 ; so the 
number of cylinders required would be as 26 : 30, which in 

this case would be 40 X — 35. 

30 



40 KNITTING CALCULATIONS 

(191) Feeds and Pounds Production 

Theoretically, the production of a knitting machine is 
proportional to the number of its feeds ; that is, a machine with 
4 feeds will produce twice as much as a machine with 2 feeds. 
But in practice the machine with 4 feeds will have to be 
stopped twice as often to piece the yarn. When the yarn is 
well wound on large bobbins or cones, this extra stoppage may 
be negligible for small differences in the number of feeds; but 
for large differences the stoppage is considerable. However, 
in any case, the stoppage to piece ends is generally provided 
for in the lost-time item; and that is usually estimated, be- 
cause the conditions are special rather than general. 

(192) Example. A 4-feed machine has room for another 
feed. What increase in production may be expected if it is 
equipped with another feed? 

The production is proportional to the number of feeds, and 
that proportion is as 5 : 4; 5 -f- 4 = 1.25; therefore, a 25% 
increase may be expected. 

(193) Example. A mill equipped with 400 feeds is making 
5,000 pounds of webbing a day. How many extra feeds will 
be required to make 6,000 pounds per day? 

400 X — — = ^ = total number of feeds needed = 480. 
5000 5 

So 80 extra feeds will be required. 



(194) Speed and Pounds Production 

The speed has a direct influence on the production ; that is, 
the production is proportional to the speed, provided that the 
latter is not excessive for the conditions. If the cylinders are 
untrue, the needles are not properly spaced or aligned, the 
stopping devices are inadequate, etc., then increase in speed may 
actually decrease the production by causing excessive stoppage; 
but when the machines are in good condition, a considerable 
range of speed is feasible without much change in necessary 
stoppage. 

(195) Example. A knit-goods manufacturer who is run- 
ning his machines at an average speed of 35-revolutions per 



KNITTING CALCULATIONS 41 

minute is advised that they may be run at 40. What increase in 
production will be occasioned by the contemplated change. 

40 -f- 35 = 1.14. The increase to be expected is 14%. 

(196) Example. A mill manager has talked "more produc- 
tion" to his boss knitter until he dares not say any more on 
the subject; yet he wants more production but does not want to 
add to his equipment. He decides to tell the engineer to speed 
up the knitting-room main-line shaft on Sunday and say nothing 
about the change. The room is turning out 4,000 pounds of 
goods, and an increase of 200 pounds will be satisfactory. The 
shaft is making 180 turns. How many turns should it make to 
give the desired increase in production? 

(Original turns) (Required production) 

4200 

180 X = 189, the required number of turns. 

4000 

(Original production) 



(197) Cut and Pounds Production 

The cut — needles per inch — affects the production in direct 
proportion; that is, 11 cut produces 10% more than 10 cut, of 
course when other conditions are unchanged. This would not 
be the case if the yarn was not looped as it is drawn in ; since 
the needle speed is not changed, and since we draw one more 
stitch in an equal time with the 11 cut than with the 10 cut, 
10% more yarn is drawn into the machine. 

(198) Example. A manufacturer learned that he could 
make an improvement in the appearance of his goods, and not 
encounter any disadvantage, by using a finer cut; so he changed 
from 11 cut to 12 cut. Unexpectedly his production increased. 
What was the amount of the increase? 

12 -f- 11 = 1.09. The amount of the increase was 9%. 

(199) Example. After a mill has been sold up for a 
season, it is discovered that the yarn is too heavy for the gage, 
but the yarn cannot be changed. In order to avoid excessive 
waste, it is contemplated to change the gage from 20 to 18. 
How will that affect the production? 

18 -=- 20 = .90. The loss in production will be 10%. 



42 KNITTING CALCULATIONS 

(200) Yarn and Pounds Production 

Increase in the yarn number results in decrease in the 
pounds production. This is because the yarn number is an 
inverse measure of the yarn weight ; that is, as the number runs 
higher the weight runs lower. Therefore, to use the yarn 
number in our weight calculations we have to use it as a divisor. 
We may either divide directly, or express the division as a 
fraction with the yarn number in the denominator. 

(201) Example. A manufacturer who is in the market 
for number 18 yarn is offered a bargain lot of number 20 yarn 
and is in a position to substitute it without making any changes 
in equipment and operation. How will his production in pounds 
be affected? 

We are calculating on a change from number 18 yarn, so 
1 8 is our basis of calculation. The change in weight is inversely 

as the number of the yarn, so our other factor is — 

20. 

18 X -=-— .90. Therefore the production will fall off 10%. 
20 

(202) Example. A mill using number 24 yarn knits 3,000 
pounds of goods per day, A new lot of nominal 24 yarn is 
really 2 3 1/2- What effect will it have on the production? 

Nominal production Nominal yarn Actual production 

24 

3000 X — 3064. 

231/a 

Actual yarn 

The production will be increased by about 64 pounds. 



(203) Stitches Per Foot and Pounds Production 

The stitches per foot of yarn affect the production 
inversely, as the yarn number does, and for the same reason; 
as the stitches per foot increase the amount of yarn used 
decreases. 

(204) Example. In order to increase the number of 
courses in the fabric, the knitter is required to shorten the 
stitch from 74 to one foot of yarn, to 80. Thereafter the 



KNITTING CALCULATIONS 43 

knitter is called to account for a falling-off in the production. 
How much of the falling-off can he lay to the change in stitch? 

New production : old production = • 

80 74 
New production = old production X 74 -r- 80 

= .925 X old production. 

Therefore, the knitter can lay iy%% of the falling-off in the 
production to the change in stitch. 

(205) Example. Some 4-inch machines which have been 
run at 45 stitches per foot of yarn are to be used to make sani- 
tary tubing at 33 stitches per foot. How will the production 
be affected? 

New production : old production = — • — 

33 45 

New production = old production X 45 -4- 33 

= 1.36 X old production. 

The production will be increased 36%. 



(206) Time and Pounds Production 

It should be understood without the saying that the produc- 
tion is proportional to the time the machine runs; so examples 
are not necessary to show the influence of time. 



(207) General Solution for Pounds Production 

We have seen that the production varies directly as the 
diameter of the machine, the feeds, the revolutions, the cut, and 
the time, and varies inversely as the yarn number and the 
stitches; and we have worked out special problems in each 
case, except for time, in which case problems were unnecessary. 
But how about the general case in which all the factors may 
vary? That is solved by a combination of all the special cases. 
We write: 



44 KNITTING CALCULATIONS 

Production varies as Diameter, Feeds, Revolutions, Cut, 
1 1 



— , Time. 



Yarn Stitches 

Expressed mathematically, that would be : 

Production varies as, Diameter X Feeds X Revolutions X 

Yarn Stitches 

Or production varies as 
Diameter X Feeds X Revolutions X Cut x Time 
Yarn X Stitches 

or the actual pounds production = 

Diameter X Feeds X Revolutions X Cut X Minutes 
800 x Yarn X Stitches 

Care should be exercised to use the right units. 

The diameter is inches measured on the needle line, 

The revolutions are per minute, 

The cut is needles per inch, 

The yarn is cotton number, 

The stitches are cylinder stitches per foot of yarn. 

The number 800 — called the constant — is necessary to 
adjust the relationship of the units used. For instance, if the 
time unit is hours, the constant must be divided by 60, making 
it 13.3 ; and if the time unit is ten-hour days, the constant must 
be divided by 600, making it 1.33. Anyone may derive his 
special formula from this general formula. 

A word of warning in respect to this formula may not be 
out of place. A couple of knitters, convinced that guesses — 
their guesses — were superior to calculations, tested this formula 
one time by actual trial and found it to be wrong, much to their 
satisfaction; and they told many of their friends about it, not 
realizing that they had confessed their inability even to conduct 
an experiment accurately, much less than to guess accurately. 
And mind you, they were "practical knitters," too ; the kind 



KNITTING CALCULATIONS 45 

that say, when asked a question, "I don't know ; but I will make 
a piece of cloth and find out." This pair demonstrated that, in 
spite of "making a piece," they found out what was not so. In 
short, the formula is absolute: what discrepancy there may be 
between the calculated and actual performance of the machine 
will be either error in the use of the formula or inaccuracy in 
the determination of the factors. 

(209) Example. What will be the production under the 
following conditions : 

Diameter of cylinder 16 inches 

Feeds 6 

Revolutions 44 

Cut 11 

Time 9 hours 540 minutes 

Yarn 20 

Stitches per foot of yarn 44 

(210) Diameter X Feeds X Revolutions X Cut X Minutes 

800 X Yarn X Stitches 
= Production in pounds. 

16 X 6 X 44 X 11 X 540 

= 35.6 

800 X 20 X 44 



(211) Pounds Production for Multiple-Thread Work 

When the work is multiple thread, the single equivalent 
yarn may be used if the stitches are alike; but for unlike 
stitches, the simplest method is to solve for the production of 
each yarn with its own stitch and to add the results. Backing 
threads are generally figured as a proportion of the face. For 
instance, flat fleeces run about 50% backing. The production 
of the face fabric is obtained by solving for the production with 
the face thread and then with the binder, or with the single 
equivalent thread if the stitches are alike. Then that weight 
is doubled to include the backing, or is increased by whatever 
proportion the backing is of the face fabric. 



46 KNITTING CALCULATIONS 

(212) Simple Solution for Pounds Production 

Attention has been called to the inadequacy of the prevalent 
yarn-numbering systems for the knitter. In order to use the 
yarn number, the square root must be obtained, and that is 
generally a decimal, inconvenient to use at best and out of the 
question for mental calculations. This is a serious obstacle to 
the advancement of the knitting industry, for most of its 
formulas are simple and they are particularly adaptable to 
mental solution. This inadequacy of the yarn-numbering system 
for the knitter is shown not only by its inconvenience in most 
cases, but by the rarity of the cases in which it is convenient. 
Of the approximately 170 simple formulas available for the 
knitter's use, the yarn number is usable conveniently only once : 
that is in the calculation of the production in pounds. In the 
other cases, its square root must be used. We come to the 
consideration of that exceptional case now. 

Efficiency is one of the most important questions in life, 
and the indications are that it will ever increase in importance ; 
and production is one of the most important elements of 
efficiency. Even the price of a machine is a secondary consider- 
ation to its capacity; and when we ask the operator of a 
machine, "What is this machine capable of producing?" and he 
says, "Well, I don't know, but I am getting 40 pounds a day 
from it," we are not seriously impressed with that operative's 
knowledge of his business. Especially, if to supply this infor- 
mation, the rule for the capacity of knitting machines is the 
simple one in which the yarn number may be used just as it is 
— that is, without extraction of the square root. We come to 
that rule by contraction of the general production formula, 

(213) Production in pounds = 
Diameter X Feeds X Revolutions X Cut X Minutes 
800 X Yarn X Stitches 

Altho this is an absolute expression, it is too cumbersome for 
solution by inspection; so we must make some assumptions in 
order to reduce it to a simple form. The reader should know 
just what these assumptions are, so that he will not deceive 
himself in the use of the simple rule. Each item will be 
treated separately. 



KNITTING CALCULATIONS 47 

The needle speed of any one type of machine is — or should 
be — practically constant. That is, we have an agreed number 
of revolutions for the average size: smaller sizes are speeded 
up, and larger sizes are speeded down, to make the needle 
velocity practically the same on all sizes. In other words, as 
the diameter of the machine goes up, the revolutions go down ; 
so for any one type of machine the product of the diameter and 
the revolutions is constant. Let us take body rib machines for 
which 35 revolutions of a 20-inch cylinder is good average 
practice. The product of the two factors is 700 ; so we may 
substitute 700 in the place of these two factors in the equation. 

The number of feeds varies roughly according to the size 
of the machine, so we may adapt our formula to 1 feed, and 
multiply the result by the number of feeds on the particular 
machine under consideration. 

The cut and the stitches are generally both increased or 
decreased proportionately according to the yarn used; so they 
may be displaced by a constant, as in the case of the diameter 
and the revolutions. 

The time may be made anything that we choose : ten hours 
is a good time to take, because it facilitates percentage deduc- 
tion both for a nine-hour or eight-hour day, and for lost time. 

The only variable factor left is the yarn number in the 
denominator of the fraction. 

It is not necessary to give the reduction of the constant. 
For good average practice for rib body machines it is 131; 
so our expression is, 

(214) Production of rib machine = 131 -f- Yarn number. 

This is the convenient form of the expression for the pro- 
duction of knitting machines. It is simpler, and generally, more 
reliable, than similar rules in use for most other machines. It 
is based on the assumptions that the needle speed is standard, 
and that the cut and the stitches per foot of yarn have a standard 
relation to the size of the yarn. That relation in this case is 
that the (215) stitches = 9.8V Yarn number, and (216) Cut 
= Stitches -^ 4, which relations will be found to conform to 
good average practice. If these relations are exactly main- 
tained, this short rule is absolute, the same as the longer rule. 
If there is considerable variation from these conditions, the 



48 KNITTING CALCULATIONS 

machine is not operating to good advantage. In the former case 
the rule is reliable as to the actual production; in the latter 
case it is an indicator of what should be expected if good 
average practice is followed. 

(218) Example. What is the ten-hour capacity of a body 
rib machine having 8 feeds and running number 24 yarn? 

131 -^- 24 = The capacity of one feed = 5.5, so the 
capacity of the eight feeds is 5.5 X 8 = 44. 

(219) Example. The ten-hour capacity of a machine is 
44 pounds, but the actual production is 35 pounds. What is 
the lost time in hours and in percentage of the whole time ? 

44 — 35 = The loss in pounds = 9. 

9 -r- 44 = The proportional loss in pounds = .204, prac- 
tically 20%. The loss in time will be the same, so the machine 
has been standing idle for two hours out of the 10. 

The capacity of a knitting machine, and the rule for it may 
be obtained from observation of the machine. For instance: 

(220) Example. An 8-feed rib machine using number 
22 yarn was timed for 30 minutes, during which interval it 
made 2.4 pounds of cloth. There were 4 stops which totaled 
3 minutes and 20 seconds. What is the 10-hour capacity of 
this machine? 

The actual running time was 30 minutes minus 3.33 
minutes, which equals 26.67 minutes. 
There are 600 minutes in 10 hours. 

(Pounds knit in 26.67 minutes) (Minutes in day) (Minutes in test) (Pounds in day) 

2.4 X 600 -4- 26.67 = 54 

(221) Example. What is the capacity rule for this 
machine? The capacity per feed is 54 -4- 8 = 6.75. 

(222) Since capacity = Constant -^ Yarn 

Constant = Capacity X Yarn 
— 6.75 X 22 
= 148.5; say 148 

148 
The rule is, Capacity — 



Yarn number 



KNITTING CALCULATIONS 49 

Attention is called, in this connection, to the fact that the 
rule is not intended for change of yarn on any one machine, 
without corresponding change of cut. For instance, the constant 
148 would hold for this machine and number 26 yarn, only 
if the cut is made correspondingly finer; which is not likely 
to be the case. In other words, the rule is not intended for 
changes of yarn in any one machine without corresponding 
change of cut; but it is intended to give a reliable idea of what 
may be expected of knitting machines in general. The 
machine in question was in a mill which prided itself on high 
speed. If the other machines in the room were operated at the 
same needle speed and at a corresponding stitch, then this 
constant, namely 148, would apply for each machine. 

(223) Example. If the average capacity constant is 131 
and a mill shows a capacity constant of 148 on account of 
higher speed, what is the gain in production, provided there 
is no increase in the lost time? 

148 — 131 — 17 
17 -r- 131 — .13. The gain is 13% 

The capacity formula for flat- work, loop- wheel machines is, 

(224) Capacity = 161 -=- The yarn number. 

It is interesting in this connection to recall the arguments 
of the respective champions of the loop-wheel and latch-needle 
machine. "My machine will produce more goods than yours 
will." ''But your cut is different." "Well, your yarn is differ- 
ent." Of all the non-conclusive arguments — and most are such 
— this was one of the leaders. The trouble was that there was 
no basis of comparison. Such questions are soon settled by the 
calculations just given, or similar ones. 

(225) Example. The capacity constant of a loop-wheel 
machine is 161 and it has 4 feeds. The capacity constant of 
a rib machine is 131 and it has 6 feeds. Which will turn off 
the greater weight of goods in a given running time with a 
given yarn, and what is the percentage gain of the one over 
the other? 



50 KNITTING CALCULATIONS 

Since the yarn is the same, the relative production is as 
the products of the respective constants and feeds. 

For the loop-wheel machine we have 161 X 4 = 644. 
For the rib machine we have 131 X 6 = 786. 

The rib machine leads, and the percentage gain is 142 -4- 644, 
or 22%. 

(226) Example. What production in pounds per feed 
should be expected of a flat-work loop-wheel machine with 
number 20 yarn? 

161 ~ 20 =8.05. Say, 8 pounds. 

(227) Example. A mill spins 2,000 pounds of number 
20 yarn per day. How many 8-feed rib machines will be 
required to knit the product? 

The single feed, 10-hour production rule for a rib machine 
is 131 -r- yarn number. 131 ~ 20 = 6.55. Allow 20% lost 
time. Then each feed will knit in pounds 6.55 x -80 = 5.24. 
So an 8-feed machine will knit in pounds 5.24 X 8 = 41.92. 
The number of machines required will be the quantity of yarn 
to be knit, namely, 2,000, divided by the capacity of each 
machine, namely, 41.92. 2,000 -^ 41.92 = 48, the number of 
8-feed rib machines required. 

(228) Example. A rib machine runs 10 hours per day; 
its average daily production is 35.85 pounds; a half -hour run 
with no lost time shows it would produce 55.9 pounds in ten 
hours actual time. How much time does it lose? 

Theoretical production Actual production Lost production 

55.9 — 35.85 = 20.05 

Lost production Theoretical production Per cent of lost time 

20.05 -f- 55.9 = .36 



(229) Linear- Yards Production 

The production in linear yards is ascertained by dividing 
the number of courses made by the machine by the number of 
courses per yard. The number of courses made by the machine 
is the revolutions per minute, multiplied by the number of 



KNITTING CALCULATIONS 51 

feeds, multiplied by the number of minutes taken, say 540, 
which is the number in a nine-hour day. The number of 
courses per yard is the courses per inch in the fabric multiplied 
by 36, the number of inches in a yard. 

(230) Example. A 17-inch machine having 6 feeds makes 
41 revolutions per minute, and the fabric has 21 courses per 
inch. How many linear yards will it make in 9 hours actual 
running time? 

Revolutions X Feeds X Minutes = 41 X 6 X 540.. (1) 
Courses per inch X 36 = 21 X 36 (2) 

(1) -f- (2) = 175.7, The linear-yards production. 



(231) Square- Yards Production 

The square-yards production is the number of stitches 
made in a given time divided by the number of stitches per 
square yard. (1), Multiply together the number of needles 
(Which produce face stitches — e.g., not dial needles), feeds, 
revolutions, and minutes; and, (2), divide (1) by the number 
of stitches per square inch multiplied by 1,296, the number of 
square inches in a square yard. 

(232) Example. What is the square-yard production 
under the following conditions? 

Needles in cylinder 754, 

Feeds 4, 

Revolutions 50, 

Time 10 hours 600 minutes 

Stitches per square inch 276 

(Face) Needles X Feeds X Revolutions X Minutes = 

754 X 4 X 50 X 600 (1) 

Stitches per square inch X Inches per square yard = 

276 X 1296 (2) 

(1) -;- (2) = 252.8, The square-yards production. 

When the speed, cut, and stitches per foot are standardized, 
the problem is simple. 



52 KNITTING CALCULATIONS 

(233) Example. How many square yards per feed may be 
expected in 10 hours actual running time from a rib machine 
with number 16 yarn? 

Number 16 yarn has 42 coils per half-inch. The produc- 
tion in yards is inversely proportional to the number of coils. 
In other words 

(234) Square yards per rib feed for 10 hours 

= 760 ~ i/ 2 Coils 
= 760 -~ 42 

— 18.1 

(235) Example. How many square yards per feed may be 
expected in 10 hours' actual running time from a flat-work, 
loop-wheel machine running number 16 yarn. 

(236) Square yards per flat feed for 10 hours 

— 1869 -r- 1/2 Coils 
= 1869 -T- 42 

= 44.5 



(237) The General Knit Fabric Formula 

Wales X Courses 35 



(238) 



Weight X Number X Stitches 18 



The wales and courses are the number per inch. 
The weight is pounds per square yard. 
The yarn number is the cotton count. 
The stitches are per foot of yarn. 

Care should be taken that the stitches per foot of yarn 
are the identical stitches which appear in the wales and courses. 
For instance, in rib knitting, it is customary to count the wales 
and courses which appear on only one side of the fabric. Then 
the stitches per foot should be those on the corresponding set 
of needles (for plain rib fabric, it makes no difference which 
set). 



KNITTING CALCULATIONS 53 

This formula is a necessary consequence of the structure 
of knit fabric and of the definitions of the factors involved; 
that is, the formula itself is exact; whatever error occurs will 
be from inaccurate factors or improper solution. 

For those who think that the above expression is algebraic, 
the following expression, in the form of compound proportion, 
makes it arithmetic. 





Weight 


Wales 


X 


X : 


Number 


Courses 


X 




Stitches 



(239) x : Number :: 35 : 18 



It is difficult to find a more satisfactory commercial formula 
in any industry. It may be used to solve for any factor when 
the other four are given ; to check the results of fabric analysis ; 
to verify fabric descriptions ; etc., etc. 

(240) Example. What is the weight per square yard of 
worsted fabric of the following description? 

Wales 16i/ 2 

Courses 24 

Stitches per foot 50 

Yarn number (cotton count) 6.76 

18 X Wales X Courses 

(241) = Weight 

35 X Number X Stitches 

18 X I6V2 X 24 

CT „ — — — : — .60 = Weight per square yard. 

35 X 6.76 X 50 * 

(242) Example. A certain book gives the following speci- 
fications for a representative piece of rib fabric. Are these 
specifications consistent? 

Yarn 24 

Stitches per foot 48 

Wales 25.72 

Courses 32.16 

Weight 369 



54 KNITTING CALCULATIONS 

If they are consistent they will satisfy the general knit- 
fabric expression. For variety use the compound proportion 
form. 



35 : 18 









Weight 




Wales 




X 


43) 


X 


i 


Number 




Courses 




X 
Stitches 






.369 


25.72 




X 




X 


i 


24. 




32.16 




X 
48. 





35 : 18 



The product of the means will equal the product of the extremes 
if the expression is satisfied. 

25.72 X 32.16 X 18 = .369 X 24 X 48 X 35 
14888 = 14878 

The discrepancy is less than one in a thousand, so the specifica- 
tions satisfy the expression for all practical purposes. 

The value of this kind of test may be judged from consider- 
ation of it applied to an analysis. Some of the factors can 
hardly fail to be right. Then whatever error there is in any 
of the remaining factors must be counterbalanced by a corre- 
sponding error in the rest of the remaining factors ; and the 
chances are rare for such a coincidence ; so the test has consider- 
able value, even if no one of the factors can be verified. Of 
course the value of the test increases according to the increase 
in the number of factors verified : if all are verified, there is no 
need of the test. 



(245) Winding 

The time lost during winding is not susceptible of calcula- 
tion. No one can calculate whether a girl will be slow or fast in 
tieing a knot or in replacing an empty cop or cone; nor how 
many lost ends, bad knots, or weak places the cone or cop will 
contain; nor how often belts must be laced; etc. Consequently, 



KNITTING CALCULATIONS 55 

this lost time must be estimated. It is convenient to estimate it 
as a percentage of the daily running time. Sometimes it is 
estimated to be one hour a day, or ten per cent. 

The capacity of the winder during actual running time is 
susceptible of very satisfactory calculation on account of the 
fact that most winders in use take an equal length of yarn per 
spindle in an equal time. That is, in a day a spindle of any 
particular winder will wind just as many yards of a No. 1 
yarn as it will of a No. 2 yarn. Of course, that number of 
yards depends on the speed at which the winder is run. Each 
type of winder is supposed to run at a certain speed recom- 
mended by the maker; but in actual practice it is generally 
run at the speed dictated by the requirements of the user, so it 
is better not to depend on the conventional speed, but to take 
the yardage wound just as we find it. 

If the capacity in yards suited our purpose the problem 
would be about as simple as it possibly could be. The capacity of 
a certain winder would then be the fixed capacity per spindle 
multiplied by the number of spindles, of course discounted for 
lost time according to the circumstances. But we want the 
capacity in pounds. 

Suppose that we wind No. 10 yarn on one spindle con- 
tinuously all day long, and find that 5 pounds were wound 
altogether. We know that No. 20 yarn has twice as many yards 

10 
per pound, so that same spindle would wind — of 5 pounds, or 

2.5 pounds of No. 20 yarn. Similarly, if we multiply together 
the capacity with any known yarn and the number of that yarn 
and divide by the number of another yarn, we get the capacity 
with the other yarn. Evidently, we do not need to multiply the 
capacity and the known yarn every time, for it will always be 
the same. In this case it is 5 X 10 = 50. We need only 
remember that 50 divided by any yarn we want to use on that 
winder will give the capacity per spindle. This number, 50, is 
called the "winder constant." 

(246) Example. A cone of No. 20 yarn was weighed. 
Winding from it was then begun; and the starting time, the 
stopping time, and the lost time were noted. After half an hour 
of actual running time the cone was found to have lost .55 of a 
pound. What is the winder constant? 



56 KNITTING CALCULATIONS 

In 10 hours the weight would have been 20 times as much, 
or 11 pounds. Then, 

(Capacity) (Yarn number) (Constant) 

11 X 20 = 220. Consequently, 

220 

Winder capacity in pounds per spindle. 



Yarn number 



It is advisable to make a longer run in the derivation of 
the winder constant, because any error in the work is multiplied 
by 20 in this case. 

(247) Example. The capacity constant of a certain winder 
is 220; how much No. 30 cone yarn will it wind per day per 
spindle? 

(Constant) (Yarn number) (Capacity) 
220 -f- 30 = 7.33 

Deduct 5%, or .36, for lost time. 7.33 — .36 = 6.96; say, 7 
pounds. If the yarn is wound from cops, deduct more lost time, 
because cops have to be replaced more frequently than cones; 
say 10% lost time. 7.33 — .73 — 6.6 pounds. 

(248) Example. A two-sided, 40-spindle winder, the 
capacity constant of which is 183, winds 250 pounds of No. 24 
yarn in 10 hours. What is the lost time? 

Constant X Number of spindles 

(249) = Total winder capacity. 

Yarn number 

183 X 40 

= 305. Since the actual winding was only 250 

pounds, the discrepancy in weight was 305 — 250 = 55. The 
proportion of lost time was as 55 : 305, namely 18 per cent. 

(250) Example. Conditions. 

The winder capacity per spindle is 183 -f- Yarn number. 
The yarn is number 20, on cones. 
The operator tends 18 spindles. 
The lost time allowance is 3%. 



KNITTING CALCULATIONS 57 

What should the operator be paid per 100 pounds to bring 
the daily pay to $1.30? 

(Lost time) (Running time, percentage) 
1. — .03 — .97 

(Constant) (Spindles) (Running time) 

183 X 18 X .97 160, the number of 

20 pounds wound per day. 

(Yarn) 

160 pounds is 1.6 hundred- weight ; so the price to pay per 
100 pounds in order to bring the daily pay to $1.30 is 1.30 -f- 
1.6 = .81 ; say, 80 cents per hundred. 



(251) Fabric Analysis 

Analysis of fabric to determine the yarn number, stitches 
per foot, weight per square yard, etc., affords one of the best 
exercises in fabric calculations. Unnecessary duplication of work 
may be avoided by an example analysis which involves most 
of the problem likely to occur. The following analysis, from 
actual practice, of a piece of flat fleece goods involves the 
methods used for single-thread work; two-thread work, with 
either like or unlike stitches ; and backing thread work ; so the 
reader may find in it the solution of most of the problems in 
the analysis of plain knit fabric. 



(252) Rectifying the Sample 

Altho the samples generally submitted to the analyst are 
small, it is advisable to make them rectangular along wales 
and courses, unless the sample is so very small that the neces- 
sary trimming would cut away too much material. The latter 
case is so special that it is not given in detail here, as it can 
be worked out by one who has mastered the general case. 

Most knit fabric will ravel from either end; but fleeces 
(backing cloth), rib fabric, tuck work, and some other types 
ravel only from one end — the end which left the needles last — 



58 KNITTING CALCULATIONS 

so it is advisable to determine which end ravels and to make 
one full raveling across from one boundary of the sample. A 
pointed instrument or stylus like a machinist's scriber, but 
with a more slender point, is useful for raveling. The other 
end of the sample should be raveled, to rectify it, if it will ravel ; 
otherwise it should be cut along the first full course at that end. 

The boundaries along the wales must be cut — preferably 
with keen slender shears — and care should be exercised to cut 
between wales and not into them. The wales are determined 
by the loops at the raveled end. If each end ravels the true 
needle wale may not be distinguishable from the sinker wale; 
but in that case either wale will answer, as long as it is con- 
sidered as the guiding wale throughout the analysis. The end 
that ravels, or a selected one of two that ravel, is taken as the 
top of the sample; the right and left end and the bottom are 
determined thereby. 

If the backing is put in at every second course, or if there 
is any other pattern feature, disregard of which would affect 
the result of the analysis, the sample should contain an integral 
number of patterns: for instance, an even number of courses 
when the backing is put in at every other course. In that case 
an odd course must be raveled off. 



(253) Weighing the Sample 

An accurate balance is essential for fabric analysis, pre- 
ferably one that weighs to thousandths of a pound, altho a 
grains scale will serve the purpose. It should be kept free from 
dust, corrosion, and rough usage. The sample should be 
weighed twice, and the results should agree; for, since the 
sample is to be raveled away, a mistake cannot be rectified by 
again reweighing the sample as a whole. 

The sample in question weighed .00513 of a pound. 



(254) Measuring the Sample 

If the sample is rectangular, the area of it may be deter- 
mined by multiplying the length by the breadth: if it is not 
rectangular, as may be the case on account of twist in the 



KNITTING CALCULATIONS 59 

knitting, one of the long boundaries may be selected as the base, 
the distance between the two as the altitude, and, of course, the 
area will be the product of the two. 

The sample in question measured in inches 3.15 in length 
by 3.62 in depth. 

The dimensions in wales and courses should be counted 
before raveling is begun. The counting is generally done by 
means of a magnifier and the stylus. An inch aperture for the 
magnifier is advisable when much work is to be done. Other- 
wise a pocket pick glass with aperture 1/2 by Vi> mcn is satis- 
factory. An objection to the small glass is that it has to be 
moved frequently during the counting. 

The sample in question has 72 wales and 85 courses. 



Summary of Sample 

Fabric — Blue, napped, double plush. 

Size — 3.15 by 3.62 = 11.40 (area in square inches). 

Stitches — 72 wales and 85 courses: 72 X 85 = 6120 
stitches. 

(255) Raveling the Sample 

It is easy to say "ravel the sample"; but the performance 
is not always easy. Lint in the loops may impede their with- 
drawal; knots may refuse to come through; the material may 
be matted; the yarn may be tender; etc. The analyst must 
determine not to pull when the yarn refuses to come, but to 
remove the obstruction or to free the yarn in a way which will 
not break it nor distort the fabric. 

In multiple-thread work care must be taken not to mix 
the different yarns. When the yarns are different in color or 
markedly different in size, material, or construction, there is not 
much danger of mixing them. In this case, since the fabric 
was dyed in the piece, the yarns were all one color; so there 
was danger of mixing the face yarns. The backing was 
heavy weight and soft twist, and the bends in it were, of course, 
different from those of the regular knitting loop, so it could be 
distinguished readily. The position of the yarn in the fabric 



60 KNITTING CALCULATIONS 

is also a means of identifying it. The binder crosses the back- 
ing, and may readily be picked up for raveling by inserting the 
stylus between it and the backing. The face thread will gen- 
erally remain in the fabric while the binder is being withdrawn, 
altho it passes through the same loops. A receptacle, such as 
a small box, should be provided for each yarn and labeled with 
the name of the yarn to avoid confusion, especially in view of 
the fact that the work may be interrupted by failing light or the 
close of the day. 

One object of the raveling is to obtain sufficient yarn to 
give reliable weighings for the determination of the numbers, 
of the respective yarns ; so it may not be necessary to ravel the 
whole sample. Indeed, it is desirable to retain a piece of the 
sample for future reference. 

When sufficient yarn has been raveled, each lot should be 
weighed, and the remnant, if any, and the total weight should 
equal the weight of the original sample. 

The weights in the case in question were as follows : 

Weight Per cent. 

Face thread 0014 27.7 

Binder thread 00125 24.7 

Backing thread 0024 47.6 

Shrinkage 00008 Negligible 

Original weight 00513 

100. 

(256) Measuring the Yarn 

To measure the yarn a scale graduated preferably in inches 
and decimals thereof should be laid on the table. The box of 
ravelings to be measured should be brought within reach, and 
all other pieces should be moved out of reach. The piece of yarn 
should be grasped at each end, stretched as much as it would be 
on a yarn-numbering reel, as nearly as can be estimated, and 
measured by holding it near to the scale. It is almost necessary 
to have two pairs of tweezers, similar to the tweezers used to 
lift the balance weights. The fingers cannot grasp the yarn 
sufficiently near the ends to afford accurate measurement. A 
sufficient number of pieces of yarn should be measured to give 
a reliable average of the length of yarn across the sample. Ten 



KNITTING CALCULATIONS 61 

is a desirable number to measure because the average can be 
seen by inspection of the total. When one lot of yarn has been 
measured, it should be carefully replaced in its box for future 
reference and put out of reach while the next lot is measured. 

The measurements in the case in question were as follows: 

Face Binder Backing 

14.75 

14.8 13.4 

13.5 12.6 

14.5 13.4 

15. 11.5 

14.5 12.5 5.6 
15.25 12.25 5.5 

13.6 13.5 5. 
15. 14. 5. 

Total 130.9 103.15 21.1 

Pieces measured 9. 8. 4. 

Average length 14.54 12.89 5.27 



(257) Lengths of Yarns in the Sample 

The number of yards of any particular yarn in the sample 
is the number of yards in a course multiplied by the number of 
courses. Since the length in a course is generally recorded in 
inches it is necessary to divide the product just mentioned by 
the number of inches in a yard, namely, 36. 

(258) Formula: 
Average length in course, in inches X Number of courses 

Inches in yard 
= Yards in piece. 

The lengths of yarn in the sample in question were as 

follows : 

14.54 X 85 

Face thread ■ == 34.3 

36 

12.89 X 85 

Binder thread = 30.4 

36 

5.27 X 85 

Backing thread = 12.43 

36 



62 KNITTING CALCULATIONS 

(259) Determination of the Yarn Numbers 

The number of the yarn is its length in yards divided by 
840 times its weight in pounds. 



(260) Formula: 

Yards of yarn 



840 X Weight of yarn in pounds 



Yarn number. 



The numbers of the yarn in the sample in question were 

as follows: 

34.3 

Face thread = 29.1 

840 X .0014 

30.4 

Binder thread =29 

840 X .00125 

12.43 

Backing thread = 6.17 

840 X -0024 

The grain (Cohoes) of the backing is 52 -f- 6.17 = 8.43. 
The backing was evidently 8V2 grain (Cohoes) ; and the face 
and binding were evidently nominal 30 cotton number, since 
commercial yarn is generally coarser than its number. 



(261) Weight Per Square Yard of the Sample 

To find the weight per square yard of the sample, divide 
its weight by its area in inches, which gives the weight of the 
fabric per square inch ; then multiply that weight by the number 
of inches in a square yard, namely 1296. The calculation is 
generally expressed as the weight of the sample multiplied by 
the relative area of a square yard to the sample; but the 
principle is the same in either case. 



(262) Formula: 
Square inches in square yard 



X Weight of sample = Weight 



Square inches in sample 
per square yard of sample. 

The weight per square yard of the sample was as follows 

1296 

X .00513 = .583 

11.40 



KNITTING CALCULATIONS 63 

(263) Stitches Per Foot of Yarn 

The stitches per foot of yarn are obtained by dividing the 
number of wales in the sample by the number of feet in the 
average raveling. The formula is derived as follows: 

Wales -r- Feet of yarn = Stitches per foot. 

Inches in raveling 

Wales -. = Stitches per foot. 

Inches in foot 

Inches in raveling 

Wales -f- = Stitches per foot. 

12 

Wales X 12 

(264) — Stitches per foot. 

Inches in raveling 

The stitches per foot in the sample were as follows : 

12 

Face thread 72 X = 59.4 

14.54 

12 

Binder thread 72 X = 67. 

12.89 

Backing (The backing is not knit in stitches). 



(265) Wales and Courses Per Inch 

The wales per inch are the number of wales in the sample 
divided by the width of the sample; and the courses are the 
number of courses divided by the depth. 

Wales in sample 

(266) = Wales per inch 

Length of sample in inches 

Courses in sample . , 

(267) — = Courses per inch 

Depth of sample in inches 



Formulas 



The wales and courses in the sample were as follows : 

72 

— 22.8, wales. 

= 23.4, courses. 



3.15 
85 
3.62 



64 KNITTING CALCULATIONS 

(268) Verification of the Analysis 

If the results of the analysis satisfy the general knit-fabric 
formula they may be considered reliable. In this case there 
are three threads involved. The backing is treated as a propor- 
tion of the face fabric, for the backing is not formed into 
stitches as the other threads are. Consequently, only two threads 
have to be considered in the formula. If the stitches of each 
thread were alike, we could use the single equivalent thread; 
but, as the stitches are different, the complication involved in 
the reduction to a single equivalent thread may be avoided by 
the use of a test for each thread. That is the same as consid- 
ering the two-thread fabric as two single-thread fabrics. The 
weights are added to obtain the total weight. The solution will 
make the principle obvious. 

A convenient form of the general knit fabric formula for 
analysis is 

Wales X Courses [Weight per 

1.944 X Yarn number X Stitches = = [square yard 

22.8 X 23.4 

Face =.1585 

1.944 X 29.1 X 59.4 

22.8 X 23.4 

Binder = .141 

1.944 X 29 X 67 

Total calculated weight of face fabric .2995. 



The backing was 47.6% of the whole fabric. 100 — 47.6 = 
52.4, the percentage of face fabric. The calculated weight of 
the face fabric, .2995, divided by the proportion of the face 
fabric, .524, gives the calculated total weight, and this should 
be close to the actual weight determined from the sample. 

The total calculated weight is.2995-^.524 = .574. 
The actual weight determined from the sample was .583. 

The analysis may be considered sufficiently verified for 
practical purposes. 



KNITTING CALCULATIONS 65 

(270) Summary 

Analysis of sample: blue napped double plush, dyed in 
piece; cotton face, cotton waste back. 

Wales per inch 22.8 

Courses per inch 23.4 

Weight, lbs., per yard .583 



Proportions by weight 
of different yarns 



Face 


27.7 


-52.4 


Binder 


24.7 


Back 


47.6 






100. 




Face 


29.1 




Binder 


29. 




Back 


6.17 


(8. 43 grain, Cohoes standard) 



Cotton counts of yarn 

Stitches per foot, Face 59.4; Binder 67. 

(271) Warp 

Warp knitting, especially in fine gages, presents some 
problems not generally met. The following analysis of a piece 
of silk warp glove fabric illustrates these problems. The 
analysis was to determine the number of the yarn. It was 
solved by means of the general knit fabric formula, since it is 
difficult to get sufficient free yarn to weigh, and since there is 
insufficient data for reliable determination of the number of fine 
yarn by means of its diameter. 

(272) Determination of the Wales and Courses 

Since this fabric is about as fine as any with which the 
analyst has to work, a micrometer counter is preferable for 
counting the stitches. The gain therewith in time and accuracy 
would soon counterbalance the cost, if much work is to be done. 



66 KNITTING CALCULATIONS 

However, it is possible to get reliable results with a pick glass — 
preferably of one inch aperture — and a fine pointer. A needle 
forced eye-first in the end of a pine stick makes a good pointer 
for this work. 

The fabric should be laid flat on a blotter or other plane 
surface which will not allow it to slip ; and it should be allowed 
to take its position in its natural shape — not stretched or 
twisted. The stitch counting should be done in several places 
in order to obtain a fair average. Each counting should follow 
a selected wale or course, as the case may be ; and not less than 
three countings should be made in any one place. 

The wales and courses in the sample were as follows : 

Wales. Courses. 
First position j rg gg 

f 61 65 

Second position < 60 65 

I 61 65 

f 59 68 

Third position \ 59 67 

I 59 68 



Total 471 530 



Average 58.85 66.3 

58.85 X 66.3= 3900, the stitches per square inch. 



(273) Weighing the Sample 

The weighing of the sample is no different than that of 
any other sample. The weight in this case was as follows : 

Weight, 84.75 grains. 
Area, 129.10 square inches. 

Weight in grains per square yard — 
(Weight of piece) (Inches in yard) 

1296 

84.75 X = 851. 

129.1 

Weight in pounds per square yard = 

(Weight in grains) (Grains in pound) 

851 -T- 7000 = .1215 



KNITTING CALCULATIONS 61 

(274) Determining the Stitches Per Foot of Yarn 

The sample was knit with a side-to-side traverse of one 
needle space ; so, in order to ravel it, lengthwise strips two wales 
in width had to be cut out of the piece. In order to have these 
strips of uniform length, a cutting piece should be trimmed out 
along courses, and the strips should be cut off the end. Sharp 
shears are necessary ; the cutting should bisect the wales adjoin- 
ing the two-wale strip; and the length of the strip should be 
sufficient to give a reasonable length of yarn, but not too long 
to cut out successfully. The suitable length may be determined 
by practice. 

Each strip will ravel if it has been properly cut. If the 
cutting has run into the strip, the raveling will be in pieces — 
two, or more, according to the number of "run-ins." If the 
cutting has been too far away from the selected wales the 
raveling may snarl or be loaded up with lint. In any case, the 
lint from the severed stitches may cling to the raveled yarn ; but 
that is not objectionable if the yarn has straightened out, since 
only the length of yarn is desired — not the weight, as would be 
the case in an ordinary determination of the yarn number. When 
a sufficient number of ravelings has been made to afford a 
reliable determination of the average length in relation to the 
stitches, the lengths should be measured. The method of meas- 
uring is described in the analysis of the double-plush sample. 

The stitches per foot of the sample in question were as 
follows : 



(1) 


(2) 


(3) 


Length of yarn 






in inches. 


Stitches. 


(2) -f- (1) 


7.5 


120 


16. 


11.38 


156 


13.7 


11. 


156 


14.2 


11.1 


156 


14. 


10.75 


153 


14.2 


10.75 


153 


14.2 


11. 


153 


13.9 


10.87 


153 


14.1 


Total.. 84.35 


1200 


- 



68 KNITTING CALCULATIONS 

The formula for the stitches per foot when the lengths are 
expressed in inches is as follows : 

12 X Stitches in piece of yarn 

(275) Stitches per foot — — : — : — 

Length of yarn in inches 

In this case it is not necessary to average the lengths and 
stitches before they are substituted in the formula ; but we may 
use the totals, since the ratio is the same. 

12 X 1200 

Stitches per foot == = 171. 

84.35 

The third column in the tabulation is to test the corre- 
spondence of the different determinations. Evidently the cor- 
respondence increased as the work progressed; so a second 
stitch calculation was made with the last four determinations, 
as follows: 



Length of yarn 








in inches 








Stitches 


10.75 








153 


10.75 








153 


11. 








153 


10.87 








153 


43.37 


612 


> Q r fnnf 


12 


X 


612 


— 1 AQ 5 



Stitches per foot 

43.37 

Since the first stitch determination was 171 and the second, 
and supposedly more reliable determination, was 169.5, it was 
decided to use 170. 



(276) Determining the Yarn Number 

The usefulness of the general knit-fabric formula is illus- 
trated in this case, in which it is almost impossible — for a com- 
mercial analysis — to obtain sufficient yarn for a reliable weigh- 
ing. Having the weight of the piece, the stitches per foot of 



KNITTING CALCULATIONS 69 

yarn, and the wales and the courses, we are able to solve for 
the yarn number. 

(277) Cotton yarn number = 

Wales X Courses 
1.944 X Stitches per foot X Weight per square yard 

The yarn number in the sample in question was as follows : 

58.85 X 66.3 

Cotton yarn number = = 97.2. 

1.944 X 170 X -1215 

The silk numbers of the yarn are 





(Constant) ( 


Cotton number) 




Dram . . , 


305 -f- 


97.2 = 


3.14 




. . 5280 ~ 


97.2 = 


54.3 



(278) Miscellaneous Problems 

(279) Example. What can be done on a 600-needle 
(cylinder) rib machine with a yarn which by test coils 38 and 
39 per half -inch? 

The average number of coils per half inch is 38.5. 
(38.5) 3 = 1482.25. 

(280) Yarn number 

= (i/ 2 Coils) 2 -f- 110.25 — 1482 -f- 110.25 = 13.43. 

(281) Cut of machine 

= i/ 2 Coils -=- 4.2865 == 38.5 -f- 4.29 = 9. 

(282) Stitches per foot 

= 1/2 Coils -r- 1.0716 = 38.5 -4- 1.07 = 36. 

(283) Wales per inch 

= 1/2 Coils h- 2. — 38.5 -J- 2. = 19.25. 



70 KNITTING CALCULATIONS 

(284) Courses per inch 

— i/ 2 Coils -f- 1.6 = 38.5 -=- 1.6 =24.1. 

(285) Pounds per square yard 

= 18.987 -^- 1/2 Coils — 18.987 -- 38.5 = .494. 

(286) Production, pounds per feed, 10 hours 

= I4443 _^ (i/ 2 Coils) 2 = 14443 -=- 1482 = 9.74. 

(287) Production, square yards per feed, 10 hours 
= 76O.I -r- 1/2 Coils = 760 -f- 38.5 = 19.75. 

(288) Tensile strength lengthwise (strip 1-inch wide) 
= 3000 -f- 1/2 Coils = 3000 -f- 38.5 = 78. 

(289) Tensile strength crosswise (strip 1-inch wide) 
= 937.5 ~ 1/2 Coils = 937.5 ~f- 38.5 = 24.4. 

(290) Width from 600 needle cylinder 

600 X 1.1 

= (600 -f- 1/2 Coils) X 1.10 = — 17.1. 

38.5 

(Body rib machines generally make the fabric 10% wider 
than the theoretical width, hence the constant 1.10 in the width 
formula. (See section 100.) 

(291) Example. Solve the above problem by use of the 
yarn number. This facilitates comparison of the use of the 
two different units; namely, the coils per half-inch, and the 
yarn number. 

(292) Yarn number 

= (1/2 Coils) 2 -f- 110.25 = 1482 -^ 110.25 = 13.43, say 13. 

(293) Cut of machine = 2.45yNo = 2.45 X 3.6 = 8.8. 

(294) Stitches per foot = 9.8yNo = 9.8 x 3.6 = 35. 

(295) Wales per inch = 5.25yNo = 5.25 X 3.6 = 18.9. 

(296) Courses per inch = 6.56yNo = 6.56 X 3.6 = 23.6. 

(297) Pounds per square yard 

= 1.808 -v- VNo = 1.808 -r- 3.6 = .502. 



KNITTING CALCULATIONS 71 

(298) Production, pounds per feed, 10 hours 
= 131 -T- No = 131 -f- 13 — 10. 

(299) Production, square yards per feed, 10 hours 
— 72.39 -r- VNo = 72.39 -f- 3.6 = 20. 

(300) Tensile strength lengthwise (strip 1-inch wide) 

= 286 -r- VNo = 286 -f- 3.6 — 80. 

(301) Tensile strength crosswise (strip 1-inch wide) 
= 89 -f- VNo = 89 -r- 3.6 = 24.8. 

(302) Width from 600 needle cylinder 

= Half needles X width wale X 1.1. 

1 

- 300 X 4 X Q1 ,._ X 1.1 

2iyNo 

- 300 X 4 Xl.l 

= 17.4 



21 X 3.6 

Since we used 13 yarn instead of 13.43 yarn, the results 
differ slightly from those calculated from the coils. Notice that 
the yarn number may be used advantageously when a series of 
calculations are made with the same yarn number, because the 
square root needs to be extracted only once. 

We have found what may be expected when this yarn 
coiling 38.5 turns to the half-inch is used on an ordinary latch- 
needle rib machine. Let us see what variations will result from 
its use on a spring-needle loop-wheel machine. 

The change in the fabric — from rib to flat — will be one 
source of variation. Rib fabric is essentially two identical flat 
fabrics connected back to back. Consequently, the wales and 
courses will be the same ; but the rib fabric will weigh twice as 
much per square yard, and will have twice the longitudinal 
tensile strength, but will have only half the number of stitches 
per foot of yarn, because the back stitches are not counted. 

The change in the type of machine introduces variations in 
the production, because the speed and the relation of the yarn 
to the needle spacing is generally different in different machines. 
The loop-wheel machine runs at a higher needle speed than the 



72 KNITTING CALCULATIONS 

latch-needle machine, and takes a heavier yarn for the same 
needle spacing, or for the same yarn takes a narrower needle 
spacing. 

(303) Example. Suppose the yarn in the two preceding 
examples is used on a spring-needle loop-wheel machine. What 
of the above results will have to be modified. Solve by means 
of the coils per half -inch. 

Cut is not generally used to designate the needle spacing 
of loop-wheel machines. 

(304) Gage = i/ 2 Coils -j- 1.66 = 38.5 -f- 1.66 = 23. 

Stitches per foot will be twice as many because all stitches 
are counted. 

(305) Stitches per foot of yarn 

= i/ 2 Coils -f- .54 = 38.5 -4- .54 = 71. 

The pounds per square yard will be only half as much, 
for in flat fabric there is only one stitch where there are two 
in rib fabric. 

(306) Pounds per square yard 

= 9.5 _4_ i/ 2 Coils = 9.5 -r- 38.5 = .24. 

The production will be increased both because the needle 
speed is higher and because the needles are spaced more closely 
together. 

(307) Production pounds per 10 hours per feed 

= 17,755 -4- (l/ 2 Coils) 2 = 17,555 -*- 1482 = 12. 

(308) Production, square yards per 10 hours per feed 
= 1869 -r- 1/2 Coils = 1869 -f- 38.5 — 48.5. 

The tensile strength lengthwise will be halved, because 
there will be half as many threads to stand the stress. 

(309) Tensile strength lengthwise (strip 1-inch wide) 
= 1500 -r- 1/2 Coils = 1500 ~ 38.5 = 39. 



KNITTING CALCULATIONS 73 

(310) Example. Solve the above flat-fabric problems with 
the use of the yarn number, taking number 13, as before. 

(311) Gage — 6.32VNo — 6.32 X 3.6 = 22.8. 

(312) Stitches per foot of yarn 

— 19.6yNo = 19.6 X 3.6 = 70.5. 

(313) Pounds per square yard 

— .904 -4- VNo — .904 -f- 3.6 = .25. 

(314) Production, pounds per 10 hours per feed 
= 161 -5- No — 161 -=- 13 = 12.4. 

(315) Production, square yards per 10 hours per feed 
= 178 -=- VNo = 178 h- 3.6 = 49.5. 

(316) Tensile strength lengthwise (strip 1-inch wide) 
= 142.86 -r- VNo — 143 -=- 3.6 — 39.6. 

(317) Example. A ribber with 275 needles, the actual cut 
of which was 13.35, was required to knit nominal 50 two-ply 
yarn; but so much trouble was experienced in starting the 
machine, that calculations were called into question, with the 
following result. 

The yarn was found to coil 50 turns per half -inch. 

Results 

(318) Width Of fabric Calculated Actual 

= Needles -^ l/ 2 Coils = 275 ~ 50 — 5.5 5.4 

(319) Wales per inch 

= i/ 2 Coils -H 2 =50-^-2 =25. 25.5 

(320) Courses per inch 

= V2 Coils -4- 1.6 — 50 -r- 1.6 — 31.2 28. 

(321) Cut 

= 1/2 Coils ~ 4.29 = 50 -f- 4.29 = 11.65 13.35 

(322) Stitches per foot 

= 1/2 Coils -i- 1.07 = 50 -r- 1.07 = 46.7 45.5 

This example illustrates the use of knitting calculations. 
The machine in question was made to purchaser's specification. 
An experienced adjuster spent two days in getting it started, and 



74 KNITTING CALCULATIONS 

then had to run it slowly in order to run it successfully. Natur- 
ally, some of the difficulty would be laid to the newness of the 
machine ; but that did not seem to account for all of it. Was the 
remaining difficulty to be laid to the author of the specification 
or to the manufacturer? And, suppose the machine continued 
to give trouble ; should the blame be put on the purchaser or the 
manufacturer? The solution of just such problems is one of 
the important uses of knitting calculations. Much of the mis- 
understanding in the industry would be dissipated by the adop- 
tion of rational bases for agreement. 

The first important lesson to be learned is that the thick- 
ness of the yarn, and not its number, is the important 
criterion for its use on the machine. Of course, stiffness and 
compressibility also enter into the consideration. In accordance 
with the prevailing custom, this 50/2 yarn was evidently con- 
sidered to be usable the same as its single equivalent, namely 
number 25. But really it is equivalent to a heavier yarn ; for 
two fifties twisted together make a thicker thread than a 
single 25. The advisability of coiling the yarn in order to 
determine its thickness is also evident. This yarn coiled 50 
turns to the half -inch, so it was as thick as a 23 yarn. More- 
over, it was less compressible and more wiry than single 23 
hosiery yarn. The calculations show that the cut was too fine 
for average practice with even hosiery yarn. 

The next question is whether the yarn is altogether too 
heavy for the cut. A good rule for the practical heavy limit of 
yarn for machines of this class is, Yarn = (Cut) 2 -f- 8. 
The cut used in this case was 13.35; so the heavy yarn limit is 
13.35 X 13.35 -r- 8 = 22.3. So technically the 50/2, even at 
its actual thickness, is within the limit; but when we consider 
the solidity and the stiffness of the ply yarn, it is evident that 
the requirements necessitate running the machine at about the 
limit of its capability. 

The conclusion is that the specification was too exacting; 
and that the manufacturer could not properly be blamed if the 
machine failed to run properly. 

(323) Example. A fabric is knit of two yarns, number 20 
and number 30, both in the cotton count. The number 30 is 
20% wool. What is the percentage of wool in the fabric? 



KNITTING CALCULATIONS 75 

First find the proportion of number 30 yarn in the fabric. 
That is the number of the other yarn divided by the sum of the 
numbers of the two yarns. 20 -=- (20 + 30) = 20 h- 50 = .40, 
the proportion of 30 yarn in the fabric. But 20% of this 30 
yarn is wool so the proportion of wool in the fabric is .20 X -40 
= .08. The fabric is 8% wool. 

(324) Example. A spinning mill contemplates knitting 
part of its product of number 20 yarn into ribbed goods. What 
will the fabric be like ? 

(325) i/ 2 Coils = 10.5 X VYarn number = 10.5 X V 20 
— 10.5 X 4.47 — 46.93, say 47. 

(326) Wales = i/ 2 Coils -f- 2 = 47 h- 2 = 23i/ 2 . Courses 
= V2 Coils -T- 1.6 = 47 -r- 1.6 = 29.4. Weight in pounds per 
square yard = 19 -7- V2 Coils = 19 -f- 47 = .405. 

(327) Example. A sample of two-ply mercerized yarn 
coils 45 turns per half-inch. What is its cotton number con- 
sidered as a single thread ? 

(328) Yarn number = (i/ 2 Coils) 2 -f- 110.25. 

45 x 45 _i_ no _ 2025 -f- 110 = 18.4. 

(329) Example. The yarn in a gauze bandage — not 
ribbed — coils 57 turns per half-inch. It is knit 27 stitches to 
the foot of yarn. How much does the stitch vary from the 
normal ? 

(330) Yarn number = (i/ 2 Coils) 2 -=- 110.25 = 57 X 57 
-T- 110.25 = 3249 -r- 110.25 = 29. 

(331) Stitches (for flat work) = i/ 2 Coils -f- .54 = 
57 -r- .54 = 105. 

Normal stitches -r- actual stitches = 105 -f- 27 = 3.9. 
The loops are approximately 4-times as long as in regular 
fabric. 



(332) Example. A mill is making rib goods that weigh 
2!/2 pounds to the dozen out of number 24 yarn. What will be 
the effect of a change to 30 yarn, with corresponding change of 
stitch? 



76 KNITTING CALCULATIONS 

Since this is a proportional change the solution may be 
effected with the coils or even the square roots of the yarn 
numbers. The coils per half-inch for 24 yarn are 51.44 and 
for 30 yarn, 57.51. These are very nearly in the ratio of 
9 to 10, so we may use the latter figures and solve the problem 
mentally. 

The weight per square yard is inversely as these numbers ; 
that is, the fabric will be 10% lighter, practically a quarter of 
a pound per dozen. 

The production in square yards — the production in which 
we are interested in this case — will be 10% less with the 30 
yarn, provided the needle speed is maintained, and the cut is 
made 10% finer to correspond to the finer yarn. 

The 30 yarn costs 30 cents as against 26 cents for the 
other yarn, but the quantities used are as 9 is to 10; so the 
relative cost for the finer yarn is as 270 is to 260, or approxi- 
mately 4% more for the finer yarn on the basis of the same 
square-yardage. 



INDEX 



A 

Actual results, table 3 

Analysis of fabric 251 

Determination of yarn num- 
ber 259, 276 

Length of yarn in sample 257 

Measuring sample 254 

Measuring the yarn 256 

Raveling sample 255 

Rectifying sample 252 

Stitches per foot of yarn, 263, 274 

Summary 270 

Verification of analysis 268 

Wales and courses per inch, 

265, 272 

Warp fabric 271 

Weighing sample 253, 273 

Weight per square yard of 
sample 261 

B 

Bandage, gauze 329 

C 

Calculations, for materials other 

than cotton 11 

Underlying relations of 4 

Capacity, of machine, from 

actual performance 220 

General formula 222 

Loop-wheel 224, 226 

Rule, derivation from actual 

performance 221 

Winder 247, 249 

Change of cylinder size with- 
out change of production 190 

Choice of units 18 

Coils per half inch, diameter, 

and diameters 6 

For 20 yarn 110 

For 24 yarn 111 

From number 

21, 115, 121, 166, 325 

From wales 133 

How to get 7 

Should be memorized 9 

Table 8 

Per inch, from wales 132 



Comparison, of calculated and 

actual results, table 3 

Of layers of fabric in roll — 124 
Of widths of fabric 105 

Of yards per pound of strips — 169 

Constant, for 11 cut and yarns 
8.5 and 6.86 72 

For winder, from actual per- 
formance 246 

For yarn-cut rule, formula 74, 81 

Courses per inch 125 

From y 2 Coils 284 320 

From yarn number 296 

In sample 265, 272 

Formula 267 

In terms of wales 126, 130, 134 

142 

Maximum 135, 137 

With 25 yarn 127 

With yarn coiling 42 turns — 131 

Cut, and gage 60 

and pounds production 197 

Definition 61 

From yarn diameter, formula 71 
For yarn .01 inch in diameter 70 
Of 500-needle 20-inch machine 65 

Of 14-gage machine 63 

Of latch-needle and spring- 
needle rib machines for 16 

yarn 83 

Of machine, and correspond- 
ing yarn 67 

Rib, latch-needle, for yarn 
coiling 43 turns per half 

inch 68 

42 turns per half inch 85 

From y 2 Coils, formula — 

84, 117, 281, 321 

From stitches 216 

From yarn number 293 

Rib, spring-needle, from V2 

Coils 86 

For yarn coiling 42 turns 
per half inch — 87 



78 



INDEX 



D 

Derivation of yarn-cut rule con- 
stant, for external dial mach- 
ine 72 

For straight machine 79 

Description of fabric from 20 
yarn, 324 

Determination of yarn number 
in analysis 259, 276 

Diameter of cylinder, effect on 

production 187 

Of yarn, diameters, and coils 6 

From number 15, 19, 139 

From V-i Coils 22 

Influence of 5 

Numbers 16, 93, 107 

Diameters lof yarn, diameter, 

and coils 6 

From diameter 140 

From number 20 

Per half inch, table 8 

Diametral revolutions, definition 25 

E 

Effect of change of yarn 332 

F 

Fabric (s), analysis 251, 271 

Character 144 

Courses per inch 125, 126 

127, 130, 131, 134, 135, 137, 142 

Description, from 20 yarn 324 

Details, with nominal 14 yarn 3 
Double thicknesses per inch 

from y 2 Coils 124 

General formula 237, 238, 239 

Good 138 

Layers in roll 122 

Regular 12 

Sleazy 143 

Stitches per foot 

147, 149, 150, 151, 152, 153, 156 

Strength 14, 175 

Thickness 118 

Thicknesses in pile 119,120 

Per inch, from x / 2 Coils __123 



Fabrics (continued) 
Two-thread, proportion of wool 

and cotton 323 

Variation of width due to dif- 
ferent machines 100 

Wales 136 

Weight 

160, 162, 163, 170, 172, 173, 174 
Width, 99, 101, 105, 106, 108, 109 
Yards per pound of strips 165 

Feeds and pounds production 191 

Examples 192 193 

Formula (s), capacity of knit- 
ting machine 222 

Of loop-wheel machine 224 

Coils per half inch from num- 
ber 21, 115, 121, 166, 325 

Formula (s), constant, for yarn- 
cut rule _74, 81 

Courses per inch, from % 

Coils 284, 320 

From yarn number 296 

In sample 267 

In terms of wales 126 

Cut, latch-needle rib, from V2 

Coils 69, 84, 117, 281, 321 

From stitches 216 

From yarn diameter 71 

From yarn number 293 

Spring-needle rib, from % 

Coils 86 

Diameter of yarn, from num- 
ber 15, 19, 139 

From V-2 Coils 22 

Diameters of yarn, from dia- 
meter 140 

From number 20, 128 

Double thicknesses of fabric 

per inch, from V2 Coils 124 

Gage, from V 2 Coils 304 

From yarn number 311 

General knit-fabric 

237, 238, 239, 243 
Needles, from width and V2 

Coils 114 

Number of yam for fabric 
of given strength 184 



INDEX 



79 



Gage (continued) 

Pounds production 

208, 210, 213, 298 

Regular fabrics 214 

Loop-wheel from Yz Coils _307 

From yarn number 314 

Production, loop-wheel, 
square yards, from Yz 

Coils 236, 308 

From yarn number 315 

Rib, square yards, from yarn 

number 299 

Production, rib, pounds, from 

y 2 Coils 286 

Square yards, from y 2 Coils 234 
Revolutions of machine, latch- 
needle rib 26 

Spring-needle, flat work 27 

Stitches per foot, flat work, 

from diameter 154 

From y 2 Coils __150, 305, 331 

From yarn number 312 

Rib, from diameter 155 

From V-2 Coils, —148, 282, 322 

from yarn number 157, 215 

294 

Of yarn in sample 264, 275 

Strength, flat work, longitud- 
inal from V-2 Coils 309 

From yam number 316 

Rib work, longitudinal, from 

y 2 Coils 181, 288 

From yarn number 179, 300 
Rib work transverse, from 

y 2 Coils 182, 289 

From yarn number 180, 301 

Of yarn, from diameter 16 

Thicknesses per inch, from Y2 

Coils 123 

Transformation, yarn, Am- 
sterdam to Canadian 33 

Cotton to worsted 31 

Wales per inch, from V2 Coils 

98, 283, 319, 326 

From yarn diameter 96 

From yarn number 295 

In sample 266 

Weight per square yard, gen- 
eral .241, 262, 269 

Flat fabric, from Y2 Coils 

171, 306 



From yarn number 313 

Rib fabric, from Yz Coils 

161, 285 
Formula (s), weight, rib fab- 
ric, from yarn number 

13, 164, 297 
Width of fabric, from V 2 Coils 

290, 318 

From yarn number 302 

Winder capacity 249 

Yards of yarn, in pound 29 

In sample 258 

Yards per pound of strips 

167, 168 
Yarn-cut, for external dial 

machine 76 

For straight machine 82 

Yarn number, from cut 73, 78, 80 

From sample 260, 277 

From y 2 Coils 280, 292, 328, 330 



Gage, and cut 60 

Definition 62 

From y 2 Coils 304 

From yarn number 311 

Of 8-cut machine 64 

Of 988-needle, 20-inch mach- 
ine 66 

Gauze bandage 329 

General knit fabric formula — 

237, 238, 239, 243 

Examples 240, 242 

General solution for pounds pro- 
duction 207 

H 

How to get the coils per half 
inch 7 



Influence of the yarn diameter 5 

K 
Knitting calculations are inevit- 
able 1 

Knitting calculations, simplicity 

and unity 17 

Worth of 2 



80 



INDEX 



Layers of fabric in roll 122 

Length-of-a-standard-weight 

system 30 

Prominent counts, table 30 

Lengths of yarn in sample 257 

Linear yards production 229 

Example 230 

Lost time, machine 219, 228 

Winder 248 

M 

Machine (s), flat work, spring- 
needle, revolutions 27 

Loop-wheel, results different 
from latch-needle rib, from 

% Coils, 303 

From yarn number 310 

Machine (s), production 185 

Rib, latch-needle, for fabric 
16 inches wide with 14 yarn 112 

Revolutions 26 

Variation in width of fabric 113 

Machine (s), speed 24 

Materials 10 

Other than cotton 11 

Memorizing coils per half inch 9 

Measuring sample for analysis 254 
Yarn in fabric analysis 256 

Miscellaneous problems 278 

Multiple-thread work, pounds 
production 211 

N 

Needles, effective number in cir- 
cular machine 104 

Number necessary to make a 

certain width of fabric 

102, 114, 116 

Number, yarn, cotton trans- 
formed to worsted 31 

For fabric of given strength 183 

Number of machines to knit a 
given amount of yarn 227 



One of two yarns equivalent 
to a third yarn 50 



Problems, miscellaneous 278 

Product of a 600-needle rib 
machine, with yarn coiling 

38.5 turns 279 

With 13 yarn 291 

Production, linear yards 229 

Example 230 

Loop-wheel, pounds, from % 
Coils 307 

From yarn number 314 

Square yards, from % 
Coils 308 

From yarn number , 315 

Production, of knitting mach- 
ines 185 

Pounds, effect of cut 197 

Examples 198, 199 

Effect of cylinder size 186 

Examples 187, 188 

Effect of feeds 191 

Examples 192, 193 

Effect of speed 194 

Examples 195, 196 

Pounds, effect of stitches 203 

Examples 204, 205 

Effect of time 206 

Effect of yam number 200 

Examples 201, 202 

For mulitple-thread work 211 

General formula 208, 210, 213 

Example 209 

General solution 207 

Rib, from % Coils 286 

Simple formula 214, 298 

Examples 218, 219,220 

221, 222, 223, 225, 226, 227 
Simple solution 212 

Square yards 231 

Examples 232, 233, 235 

Square yards from % Coils 287 



INDEX 



81 



Proportions, two-thirds work, 
9-pound, 20-gage, plated fab- 
ric 58 

16 and 24 yarn 55 

Standard-length system 38 

Standard-weight system, equal 

stitches 53, 54 

Unequal stitches 56 

Wool and cotton 323 

R 

Raveling sample for analysis 255 
Rectifying sample for analysis 252 

Regular fabrics 12 

Relations which underlie the cal- 
culations 4 

Relative production from capa- 
city constants 223 

Formulas 225 

Revolutions of machine, latch- 
needle rib 26 

Spring-needle, flat work 27 

Rib fabric, weight 13, 161 

162, 163, 164, 285, 297 

S 

Single equivalent of two yarns 39 
Comparison of two pairs — 41 

18 and 16 45 

18 cotton and 24 worsted 44 

Of 10 and 20 40 

Of three or more yarns 46 

7.2 and 36 49 

Standard-length system 37 

10 and 15 52 

12 and 18 48 

12, 18 and 36 47 

22 and 30 43 

Two 26's 42 

Simple solution for pounds pro- 
duction 212 

Simplicity and unity of knitting 
calculations 17 

Specification of fabric 144 

Of rib machine 112 

Speed of machines 24 

And pounds production 194 

Example 195, 196 

Square roots, table 23 



Square yards production 231 

Examples 232, 233, 235 

Flat work, from % Coils 236 

Rib work, from V 2 Coils, 

formula 234 

From yarn number 299 

Stitches per foot of yarn 145 

And pounds production 203 

Determined by comparison of 

coils 146 

Of yarn diameter 152 

Flat work 150, 151, 153, 154, 159 

From y 2 Coils 305, 331 

From yarn number 312 

In sample 263, 274 

Relation to Vi Coils ___147, 148 
Rib work 149, 155, 156, 157, 158 

215 

From % Coils 282, 322 

From yarn number 294 

Strength of fabric 14, 175 

Flat, in different directions, 

ratio 176 

Longitudinal, from y 2 Coils 309 

From yarn number 316 

Rib, from yarn number 178 

Longitudinal, from y 2 Coils 

181, 288 
From yarn number, formula 

179, 300 
In different directions, ratio 177 
Transverse, from % Coils 182, 289 

From yarn number 180, 301 

Of yarn, from diameter 16 

Summary of analysis 270 

T 

Tables 

Comparison of calculated and 

actual results 3 

Diameters (and coils) per 

half inch 8 

Square roots of numbers 23 

Yarn counts, standard-length 

system 32 

Standard-weight system — 30 

Transformation constants 36 

Test of knitting specifications 242 

Thickness of fabric 118 



82 



INDEX 



Thicknesses of fabric in pile 

119, 120 

Time, and pounds production 206 

Lost 223, 228 

Transformation, Amsterdam 
standard to Canadian stand- 
ard 33 

Between the two yarn-num- 
bering- systems 34 

Table 36 

Of cotton number to worsted 

number 31 

Of worsted number to cotton 

number 59 

Of worsted number to New 
Hampshire 35 

u 

Units, choice of 18 

V 

Verification of analysis 268 

W 

Wales per inch, for 16 yarn __ 92 

For 13 yam 95 

For 25 yarn 129 

For yarn coiling 21 turns per 

half inch 97 

.015 inch in diameter 90 

From diameters per inch 141 

From y 2 Coils, 98, 136, 283, 319 

326 

From sample 265, 272 

Formula 266 

From yarn diameter, formula 96 

Number 295 

Wales 88 

Wale (s), width for 7 yarn 103 

For 16 yarn 94 

For 25 yarn 129 

For yarn .015 diameter 91 

.01 diameter 89 

Warp fabric analysis 271 

Weighing sample for analysis 

253, 273 
Weight-of-a-standard-length 

system 32 



Weight per square yard, flat 
fabric from V 2 Coils __171, 306 

From yarn number 170, 313 

Formula 241, 262, 269 

From general details 240 

From sample 261 

Irregular fabrics 172 

Regular fabrics 160 

Rib fabric, from V2 Coils 161 

162, 163, 285 

From yarn number 13, 164 

297 
Variation, for variation in 
yarn 173, 174 

What can be done on a 600- 
needle rib machine with 13 
yarn 279 

Width of fabric 99 

For change from 20 yarn to 

24 yarn ___109 

For 500 needles and 10 yarn, 

from diameter 101 

For 400 needles and 16 yarn 106 
For 175 needles and 18 yarn 105 
From yarn diameter and 

needles, formula 108 

From y 2 Coils 318 

From 600 needle cylinder 290, 302 
Variation due to different 

machines 100, 113 

Winding 245 

Examples 246, 247, 248, 250 

Price per 100 pounds for a cer- 
tain day wage 250 

Worth of knitting calculations 2 

Y 

Yards of yam in pound 29 

In sample, formula 258 

Yards per pound strip webbing 165 

Yarn, Amsterdam standard 

transformed to Canadian 33 

And cut of machine 67 

And pounds production 200 

Coils per half inch, from 

wales 133 

per inch, from wales 132 



INDEX 



83 



Yarn (continued) 

Combined with 10 to equal 

six 51 

Counts 28 

Standard length system 32 

Standard weight system — 30 
Transformation between the 
two systems, table 36 

Cotton number transformed to 
worsted number 31 

Diameter from number 

15, 19, 107, 128 

From y 2 Coils 22 

Influence of 5 

Diameters, from number 20 

Per half inch, table 8 

Effect of change 332 

Numbering systems, trans- 
formations 34 

One of two equivalent to a 
third 50 

Proportion in two-thread 
work, 9-pound, 20-gage 

plated fabric 58 

16 and 24 yarn 55 

Standard-length system 38 

Standard-weight j system,, 

equal stitches 53, 54 

Unequal stitches 56 

Stitches per foot 145, 146 

Strength from diameter 16 

Too heavy for machine 317 



Worsted number transformed 

to New Hampshire 35 

Yards in pound 29 

Yam number, for 8-cut, latch- 
needle, rib machine 77 

For fabric of given strength 183 
For straight machine, foi-mula 82 
Formula, for external dial 

machine 76 

From cut, formula 73, 80 

From y 2 Coils 280, 292, 327, 328 

330 
From sample, formula _260, 277 
30 Worsted transformed to 

cotton 59 

Yarn number, single equiva- 
lent, compai'ison of; two 26's 

and 22 and 30 41 

18 and 16 45 

18 cotton and 24 worsted 44 

In standard-length system — 37 
In standard weight system— 39 

Of 10 and 20 40 

Of three or more 46 

7.2 and 36 49 

10 and 15 52 

12 and 18 48 

12, 18, and 36 47 

22 and 30 43 

Two 26's 42 



American Directory 
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BRAGDON, LORD & NAGLE CO. 

334 Fourth Avenue New York, N. Y. 



Patented 

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